Neural-Symbolic Integration for Interpretable AI Decision Making

The integration of neural networks with symbolic reasoning represents a convergence of two fundamental approaches to artificial intelligence: the pattern recognition capabilities of deep learning and the logical reasoning power of symbolic systems. While neural networks excel at learning from data and handling uncertainty, they often lack interpretability and struggle with logical consistency. Symbolic systems provide transparency and logical rigor but can be brittle when faced with noisy or incomplete data.

Neural-symbolic integration offers a path to AI systems that combine the best of both worlds, providing interpretable decisions backed by logical reasoning while maintaining the robustness and learning capabilities of neural approaches. This comprehensive guide explores the architectural patterns, implementation strategies, and production deployment considerations for building neural-symbolic systems that meet enterprise requirements for reliability, interpretability, and performance.

Understanding Neural-Symbolic Architecture

Neural-symbolic systems can be organized along a spectrum from loose coupling to tight integration, each offering different trade-offs between interpretability, performance, and implementation complexity.

Neural-Symbolic Integration Spectrum:

Loose Coupling:
┌─────────────────┐    ┌─────────────────┐
│ Neural Network  │───▶│ Symbolic System │
│ (Pattern Recog.)│    │ (Logic Reasoning)│
└─────────────────┘    └─────────────────┘
• Independent components
• Clear separation of concerns
• Easy to debug and modify
• Potential information loss

Tight Integration:
┌─────────────────────────────────────────────────────────────┐
│ Unified Neural-Symbolic Architecture                        │
├─────────────────────────────────────────────────────────────┤
│ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐            │
│ │ Neural      │ │ Symbol      │ │ Reasoning   │            │
│ │ Perception  │ │ Grounding   │ │ Engine      │            │
│ │ Layer       │ │ Layer       │ │             │            │
│ └─────────────┘ └─────────────┘ └─────────────┘            │
│        │               │               │                   │
│        └───────────────┼───────────────┘                   │
│                        │                                   │
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Differentiable Symbolic Reasoning                       │ │
│ │ • Fuzzy logic integration                               │ │
│ │ • Probabilistic symbolic computation                    │ │
│ │ • Gradient-based rule learning                          │ │
│ └─────────────────────────────────────────────────────────┘ │
└─────────────────────────────────────────────────────────────┘
• End-to-end learning
• Optimal information flow
• Complex implementation
• High performance potential

Production Architecture:
┌─────────────────────────────────────────────────────────────┐
│ Neural-Symbolic Decision Engine                             │
├─────────────────────────────────────────────────────────────┤
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Input Processing Layer                                  │ │
│ │ • Multi-modal data ingestion                            │ │
│ │ • Feature extraction and embedding                      │ │
│ │ • Uncertainty quantification                            │ │
│ └─────────────────────────────────────────────────────────┘ │
│                             │                               │
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Neural Perception Module                                │ │
│ │ • Pattern recognition                                   │ │
│ │ • Anomaly detection                                     │ │
│ │ • Confidence estimation                                 │ │
│ └─────────────────────────────────────────────────────────┘ │
│                             │                               │
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Symbol Grounding Layer                                  │ │
│ │ • Concept extraction                                    │ │
│ │ • Semantic mapping                                      │ │
│ │ • Contextual interpretation                             │ │
│ └─────────────────────────────────────────────────────────┘ │
│                             │                               │
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Symbolic Reasoning Engine                               │ │
│ │ • Rule-based inference                                  │ │
│ │ • Constraint satisfaction                               │ │
│ │ • Causal reasoning                                      │ │
│ └─────────────────────────────────────────────────────────┘ │
│                             │                               │
│ ┌─────────────────────────────────────────────────────────┐ │
│ │ Explanation Generation                                  │ │
│ │ • Decision justification                                │ │
│ │ • Counterfactual analysis                               │ │
│ │ • Confidence intervals                                  │ │
│ └─────────────────────────────────────────────────────────┘ │
└─────────────────────────────────────────────────────────────┘

Production Neural-Symbolic Framework

Here’s a comprehensive implementation of a production-ready neural-symbolic system:

   1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
import torch
import torch.nn as nn
import numpy as np
from typing import Dict, List, Optional, Any, Union, Tuple
from dataclasses import dataclass, field
from enum import Enum
import logging
from abc import ABC, abstractmethod
import json
from collections import defaultdict
import asyncio

class ReasoningType(Enum):
    DEDUCTIVE = "deductive"
    INDUCTIVE = "inductive" 
    ABDUCTIVE = "abductive"
    CAUSAL = "causal"

class SymbolType(Enum):
    CONCEPT = "concept"
    RELATION = "relation"
    PROPERTY = "property"
    RULE = "rule"

@dataclass
class Symbol:
    """Symbolic representation with confidence and context"""
    name: str
    symbol_type: SymbolType
    confidence: float
    properties: Dict[str, Any] = field(default_factory=dict)
    relations: List[str] = field(default_factory=list)
    embedding: Optional[torch.Tensor] = None
    source: Optional[str] = None

@dataclass
class Rule:
    """Symbolic rule with conditions and conclusions"""
    id: str
    conditions: List[str]  # Logical conditions
    conclusions: List[str]  # Logical conclusions
    confidence: float
    weight: float = 1.0
    source: str = "learned"
    metadata: Dict[str, Any] = field(default_factory=dict)

@dataclass
class ReasoningStep:
    """Single step in reasoning chain"""
    step_id: str
    reasoning_type: ReasoningType
    input_symbols: List[Symbol]
    applied_rules: List[Rule]
    output_symbols: List[Symbol]
    confidence: float
    explanation: str

@dataclass
class Explanation:
    """Complete explanation of a decision"""
    decision: str
    confidence: float
    reasoning_chain: List[ReasoningStep]
    supporting_evidence: List[Dict[str, Any]]
    alternative_decisions: List[Dict[str, Any]]
    uncertainty_sources: List[str]

class NeuralPerceptionModule(nn.Module):
    """Neural module for pattern recognition and feature extraction"""
    
    def __init__(self, config: Dict[str, Any]):
        super().__init__()
        self.config = config
        
        # Multi-modal input encoders
        self.text_encoder = self._build_text_encoder()
        self.image_encoder = self._build_image_encoder() if config.get('vision_enabled') else None
        self.numerical_encoder = self._build_numerical_encoder()
        
        # Feature fusion layer
        self.fusion_layer = nn.MultiheadAttention(
            embed_dim=config['hidden_dim'],
            num_heads=config['num_heads'],
            dropout=config.get('dropout', 0.1)
        )
        
        # Uncertainty estimation
        self.uncertainty_estimator = nn.Sequential(
            nn.Linear(config['hidden_dim'], config['hidden_dim'] // 2),
            nn.ReLU(),
            nn.Linear(config['hidden_dim'] // 2, 1),
            nn.Sigmoid()
        )
        
        # Symbol detection heads
        self.concept_detector = nn.Sequential(
            nn.Linear(config['hidden_dim'], config['num_concepts']),
            nn.Sigmoid()
        )
        
        self.relation_detector = nn.Sequential(
            nn.Linear(config['hidden_dim'] * 2, config['num_relations']),
            nn.Sigmoid()
        )
        
    def _build_text_encoder(self):
        """Build text encoding component"""
        from transformers import AutoModel
        
        model_name = self.config.get('text_model', 'bert-base-uncased')
        encoder = AutoModel.from_pretrained(model_name)
        
        # Freeze pre-trained weights if specified
        if self.config.get('freeze_text_encoder', False):
            for param in encoder.parameters():
                param.requires_grad = False
        
        return encoder
    
    def _build_image_encoder(self):
        """Build image encoding component"""
        from torchvision import models
        
        encoder = models.resnet50(pretrained=True)
        # Remove final classification layer
        encoder = nn.Sequential(*list(encoder.children())[:-1])
        
        if self.config.get('freeze_image_encoder', True):
            for param in encoder.parameters():
                param.requires_grad = False
        
        return encoder
    
    def _build_numerical_encoder(self):
        """Build numerical data encoder"""
        input_dim = self.config.get('numerical_input_dim', 10)
        hidden_dim = self.config['hidden_dim']
        
        return nn.Sequential(
            nn.Linear(input_dim, hidden_dim // 2),
            nn.ReLU(),
            nn.Dropout(self.config.get('dropout', 0.1)),
            nn.Linear(hidden_dim // 2, hidden_dim),
            nn.ReLU()
        )
    
    def forward(self, inputs: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
        """Forward pass through neural perception"""
        
        encoded_features = []
        feature_types = []
        
        # Encode text features
        if 'text' in inputs:
            text_features = self.text_encoder(**inputs['text']).last_hidden_state
            # Pool text features
            text_features = torch.mean(text_features, dim=1)
            encoded_features.append(text_features)
            feature_types.append('text')
        
        # Encode image features
        if 'image' in inputs and self.image_encoder:
            image_features = self.image_encoder(inputs['image'])
            image_features = image_features.flatten(start_dim=1)
            encoded_features.append(image_features)
            feature_types.append('image')
        
        # Encode numerical features
        if 'numerical' in inputs:
            numerical_features = self.numerical_encoder(inputs['numerical'])
            encoded_features.append(numerical_features)
            feature_types.append('numerical')
        
        if not encoded_features:
            raise ValueError("No valid input features provided")
        
        # Fuse features using attention
        if len(encoded_features) > 1:
            # Stack features for attention
            stacked_features = torch.stack(encoded_features, dim=1)
            fused_features, attention_weights = self.fusion_layer(
                stacked_features, stacked_features, stacked_features
            )
            # Global pooling
            fused_features = torch.mean(fused_features, dim=1)
        else:
            fused_features = encoded_features[0]
            attention_weights = None
        
        # Estimate uncertainty
        uncertainty = self.uncertainty_estimator(fused_features)
        
        # Detect concepts
        concept_scores = self.concept_detector(fused_features)
        
        # Detect relations (using pairwise features)
        batch_size = fused_features.shape[0]
        relation_features = torch.cat([
            fused_features.unsqueeze(1).expand(-1, batch_size, -1).reshape(-1, self.config['hidden_dim']),
            fused_features.unsqueeze(0).expand(batch_size, -1, -1).reshape(-1, self.config['hidden_dim'])
        ], dim=1)
        
        relation_scores = self.relation_detector(relation_features)
        relation_scores = relation_scores.reshape(batch_size, batch_size, -1)
        
        return {
            'features': fused_features,
            'uncertainty': uncertainty,
            'concept_scores': concept_scores,
            'relation_scores': relation_scores,
            'attention_weights': attention_weights,
            'feature_types': feature_types
        }

class SymbolGroundingLayer:
    """Layer for grounding neural outputs to symbolic representations"""
    
    def __init__(self, config: Dict[str, Any]):
        self.config = config
        
        # Symbol vocabularies
        self.concept_vocab = config.get('concept_vocab', [])
        self.relation_vocab = config.get('relation_vocab', [])
        
        # Grounding thresholds
        self.concept_threshold = config.get('concept_threshold', 0.5)
        self.relation_threshold = config.get('relation_threshold', 0.5)
        
        # Symbol embeddings
        self.symbol_embeddings = self._initialize_symbol_embeddings()
        
    def _initialize_symbol_embeddings(self) -> Dict[str, torch.Tensor]:
        """Initialize embeddings for known symbols"""
        embeddings = {}
        
        # Initialize concept embeddings
        for concept in self.concept_vocab:
            embeddings[concept] = torch.randn(self.config['hidden_dim'])
        
        # Initialize relation embeddings  
        for relation in self.relation_vocab:
            embeddings[relation] = torch.randn(self.config['hidden_dim'])
        
        return embeddings
    
    async def ground_symbols(self, 
                           neural_output: Dict[str, torch.Tensor],
                           context: Optional[Dict[str, Any]] = None) -> List[Symbol]:
        """Ground neural network outputs to symbolic representations"""
        
        grounded_symbols = []
        
        # Ground concepts
        concept_scores = neural_output['concept_scores']
        uncertainty = neural_output['uncertainty']
        
        batch_size = concept_scores.shape[0]
        
        for batch_idx in range(batch_size):
            batch_uncertainty = uncertainty[batch_idx].item()
            
            # Ground concepts for this batch item
            for concept_idx, score in enumerate(concept_scores[batch_idx]):
                if score.item() > self.concept_threshold:
                    concept_name = self.concept_vocab[concept_idx]
                    
                    # Adjust confidence based on uncertainty
                    confidence = score.item() * (1 - batch_uncertainty)
                    
                    symbol = Symbol(
                        name=concept_name,
                        symbol_type=SymbolType.CONCEPT,
                        confidence=confidence,
                        embedding=self.symbol_embeddings.get(concept_name),
                        source='neural_perception'
                    )
                    
                    grounded_symbols.append(symbol)
            
            # Ground relations
            relation_scores = neural_output['relation_scores'][batch_idx]
            
            for i in range(relation_scores.shape[0]):
                for j in range(relation_scores.shape[1]):
                    if i != j:  # No self-relations
                        for rel_idx, score in enumerate(relation_scores[i, j]):
                            if score.item() > self.relation_threshold:
                                relation_name = self.relation_vocab[rel_idx]
                                
                                confidence = score.item() * (1 - batch_uncertainty)
                                
                                symbol = Symbol(
                                    name=f"{relation_name}({i},{j})",
                                    symbol_type=SymbolType.RELATION,
                                    confidence=confidence,
                                    properties={
                                        'subject_idx': i,
                                        'object_idx': j,
                                        'relation_type': relation_name
                                    },
                                    embedding=self.symbol_embeddings.get(relation_name),
                                    source='neural_perception'
                                )
                                
                                grounded_symbols.append(symbol)
        
        return grounded_symbols
    
    async def enhance_grounding_with_context(self, 
                                           symbols: List[Symbol],
                                           context: Dict[str, Any]) -> List[Symbol]:
        """Enhance symbol grounding with contextual information"""
        
        enhanced_symbols = []
        
        for symbol in symbols:
            enhanced_symbol = Symbol(
                name=symbol.name,
                symbol_type=symbol.symbol_type,
                confidence=symbol.confidence,
                properties=symbol.properties.copy(),
                relations=symbol.relations.copy(),
                embedding=symbol.embedding,
                source=symbol.source
            )
            
            # Add contextual properties
            if 'domain' in context:
                enhanced_symbol.properties['domain'] = context['domain']
            
            if 'timestamp' in context:
                enhanced_symbol.properties['timestamp'] = context['timestamp']
            
            # Adjust confidence based on context
            if 'domain_confidence_multiplier' in context:
                multiplier = context['domain_confidence_multiplier'].get(
                    symbol.name, 1.0
                )
                enhanced_symbol.confidence *= multiplier
            
            enhanced_symbols.append(enhanced_symbol)
        
        return enhanced_symbols

class SymbolicReasoningEngine:
    """Symbolic reasoning engine with multiple reasoning strategies"""
    
    def __init__(self, config: Dict[str, Any]):
        self.config = config
        
        # Rule base
        self.rules: Dict[str, Rule] = {}
        self.rule_dependencies: Dict[str, List[str]] = defaultdict(list)
        
        # Reasoning strategies
        self.reasoning_strategies = {
            ReasoningType.DEDUCTIVE: self._deductive_reasoning,
            ReasoningType.INDUCTIVE: self._inductive_reasoning,
            ReasoningType.ABDUCTIVE: self._abductive_reasoning,
            ReasoningType.CAUSAL: self._causal_reasoning
        }
        
        # Load initial rule base
        self._load_rules(config.get('initial_rules', []))
        
    def _load_rules(self, rules_config: List[Dict[str, Any]]):
        """Load rules from configuration"""
        
        for rule_config in rules_config:
            rule = Rule(
                id=rule_config['id'],
                conditions=rule_config['conditions'],
                conclusions=rule_config['conclusions'],
                confidence=rule_config.get('confidence', 1.0),
                weight=rule_config.get('weight', 1.0),
                source=rule_config.get('source', 'config'),
                metadata=rule_config.get('metadata', {})
            )
            
            self.rules[rule.id] = rule
            
            # Build dependency graph
            for condition in rule.conditions:
                self.rule_dependencies[condition].append(rule.id)
    
    async def reason(self, 
                   symbols: List[Symbol],
                   reasoning_type: ReasoningType = ReasoningType.DEDUCTIVE,
                   max_steps: int = 10) -> Tuple[List[Symbol], List[ReasoningStep]]:
        """Perform symbolic reasoning on grounded symbols"""
        
        reasoning_strategy = self.reasoning_strategies.get(reasoning_type)
        if not reasoning_strategy:
            raise ValueError(f"Unknown reasoning type: {reasoning_type}")
        
        return await reasoning_strategy(symbols, max_steps)
    
    async def _deductive_reasoning(self, 
                                 symbols: List[Symbol],
                                 max_steps: int) -> Tuple[List[Symbol], List[ReasoningStep]]:
        """Forward chaining deductive reasoning"""
        
        derived_symbols = symbols.copy()
        reasoning_steps = []
        
        # Create working memory of facts
        working_memory = set()
        for symbol in symbols:
            if symbol.symbol_type in [SymbolType.CONCEPT, SymbolType.RELATION]:
                working_memory.add(symbol.name)
        
        for step in range(max_steps):
            step_derived = []
            applied_rules = []
            
            # Try to apply each rule
            for rule_id, rule in self.rules.items():
                if self._can_apply_rule(rule, working_memory):
                    # Apply rule
                    new_conclusions = self._apply_rule(rule, derived_symbols)
                    
                    if new_conclusions:
                        step_derived.extend(new_conclusions)
                        applied_rules.append(rule)
                        
                        # Add to working memory
                        for conclusion in new_conclusions:
                            working_memory.add(conclusion.name)
            
            if step_derived:
                # Create reasoning step
                reasoning_step = ReasoningStep(
                    step_id=f"deductive_step_{step}",
                    reasoning_type=ReasoningType.DEDUCTIVE,
                    input_symbols=derived_symbols.copy(),
                    applied_rules=applied_rules,
                    output_symbols=step_derived,
                    confidence=self._calculate_step_confidence(applied_rules),
                    explanation=self._generate_step_explanation(applied_rules, step_derived)
                )
                
                reasoning_steps.append(reasoning_step)
                derived_symbols.extend(step_derived)
            else:
                # No new derivations possible
                break
        
        return derived_symbols, reasoning_steps
    
    def _can_apply_rule(self, rule: Rule, working_memory: set) -> bool:
        """Check if rule conditions are satisfied"""
        
        for condition in rule.conditions:
            if condition not in working_memory:
                return False
        
        return True
    
    def _apply_rule(self, rule: Rule, symbols: List[Symbol]) -> List[Symbol]:
        """Apply rule and generate new symbols"""
        
        new_symbols = []
        
        # Simple rule application - in practice, this would be more sophisticated
        for conclusion in rule.conclusions:
            # Check if conclusion already exists
            exists = any(s.name == conclusion for s in symbols)
            
            if not exists:
                new_symbol = Symbol(
                    name=conclusion,
                    symbol_type=SymbolType.CONCEPT,  # Simplified assumption
                    confidence=rule.confidence,
                    source=f"rule_{rule.id}",
                    properties={'derived_from_rule': rule.id}
                )
                
                new_symbols.append(new_symbol)
        
        return new_symbols
    
    async def _inductive_reasoning(self, 
                                 symbols: List[Symbol],
                                 max_steps: int) -> Tuple[List[Symbol], List[ReasoningStep]]:
        """Inductive reasoning to generate new rules"""
        
        # Analyze patterns in symbols to generate hypotheses
        pattern_analysis = self._analyze_symbol_patterns(symbols)
        
        new_rules = []
        reasoning_steps = []
        
        for pattern in pattern_analysis:
            if pattern['confidence'] > self.config.get('induction_threshold', 0.7):
                # Generate new rule from pattern
                new_rule = Rule(
                    id=f"induced_rule_{len(self.rules)}",
                    conditions=pattern['conditions'],
                    conclusions=pattern['conclusions'],
                    confidence=pattern['confidence'],
                    source='inductive_reasoning',
                    metadata={'pattern': pattern}
                )
                
                new_rules.append(new_rule)
                self.rules[new_rule.id] = new_rule
        
        if new_rules:
            reasoning_step = ReasoningStep(
                step_id="inductive_step",
                reasoning_type=ReasoningType.INDUCTIVE,
                input_symbols=symbols,
                applied_rules=new_rules,
                output_symbols=[],  # Rules don't directly produce symbols
                confidence=np.mean([r.confidence for r in new_rules]),
                explanation=f"Generated {len(new_rules)} new rules through pattern analysis"
            )
            
            reasoning_steps.append(reasoning_step)
        
        return symbols, reasoning_steps
    
    def _analyze_symbol_patterns(self, symbols: List[Symbol]) -> List[Dict[str, Any]]:
        """Analyze patterns in symbols for inductive reasoning"""
        
        patterns = []
        
        # Group symbols by type
        concepts = [s for s in symbols if s.symbol_type == SymbolType.CONCEPT]
        relations = [s for s in symbols if s.symbol_type == SymbolType.RELATION]
        
        # Look for co-occurrence patterns
        concept_pairs = []
        for i, concept1 in enumerate(concepts):
            for j, concept2 in enumerate(concepts[i+1:], i+1):
                # Check if concepts frequently co-occur
                cooccurrence_score = self._calculate_cooccurrence(concept1, concept2)
                
                if cooccurrence_score > 0.5:
                    pattern = {
                        'conditions': [concept1.name],
                        'conclusions': [concept2.name],
                        'confidence': cooccurrence_score,
                        'type': 'concept_cooccurrence'
                    }
                    patterns.append(pattern)
        
        return patterns
    
    def _calculate_cooccurrence(self, symbol1: Symbol, symbol2: Symbol) -> float:
        """Calculate co-occurrence score between symbols"""
        
        # Simplified co-occurrence based on confidence similarity
        confidence_diff = abs(symbol1.confidence - symbol2.confidence)
        return 1.0 - confidence_diff
    
    async def _abductive_reasoning(self, 
                                 symbols: List[Symbol],
                                 max_steps: int) -> Tuple[List[Symbol], List[ReasoningStep]]:
        """Abductive reasoning to find best explanations"""
        
        # Find potential explanations for observed symbols
        explanations = self._generate_explanations(symbols)
        
        # Rank explanations by plausibility
        ranked_explanations = sorted(
            explanations, 
            key=lambda x: x['plausibility'], 
            reverse=True
        )
        
        reasoning_steps = []
        additional_symbols = []
        
        if ranked_explanations:
            best_explanation = ranked_explanations[0]
            
            # Generate symbols that would support this explanation
            supporting_symbols = self._generate_supporting_symbols(best_explanation)
            additional_symbols.extend(supporting_symbols)
            
            reasoning_step = ReasoningStep(
                step_id="abductive_step",
                reasoning_type=ReasoningType.ABDUCTIVE,
                input_symbols=symbols,
                applied_rules=[],
                output_symbols=supporting_symbols,
                confidence=best_explanation['plausibility'],
                explanation=f"Best explanation: {best_explanation['description']}"
            )
            
            reasoning_steps.append(reasoning_step)
        
        return symbols + additional_symbols, reasoning_steps
    
    def _generate_explanations(self, symbols: List[Symbol]) -> List[Dict[str, Any]]:
        """Generate potential explanations for observed symbols"""
        
        explanations = []
        
        # Simple explanation generation based on rules
        for rule in self.rules.values():
            # Check if any rule conclusions match observed symbols
            matching_conclusions = []
            for symbol in symbols:
                if symbol.name in rule.conclusions:
                    matching_conclusions.append(symbol.name)
            
            if matching_conclusions:
                # This rule could explain the observed symbols
                explanation = {
                    'rule_id': rule.id,
                    'description': f"Rule {rule.id} explains {matching_conclusions}",
                    'plausibility': rule.confidence * len(matching_conclusions) / len(rule.conclusions),
                    'missing_conditions': [c for c in rule.conditions if not any(s.name == c for s in symbols)]
                }
                explanations.append(explanation)
        
        return explanations
    
    def _generate_supporting_symbols(self, explanation: Dict[str, Any]) -> List[Symbol]:
        """Generate symbols that would support an explanation"""
        
        supporting_symbols = []
        
        # Generate symbols for missing conditions
        for condition in explanation.get('missing_conditions', []):
            symbol = Symbol(
                name=condition,
                symbol_type=SymbolType.CONCEPT,
                confidence=explanation['plausibility'],
                source='abductive_reasoning',
                properties={'supports_explanation': explanation['rule_id']}
            )
            supporting_symbols.append(symbol)
        
        return supporting_symbols
    
    async def _causal_reasoning(self, 
                              symbols: List[Symbol],
                              max_steps: int) -> Tuple[List[Symbol], List[ReasoningStep]]:
        """Causal reasoning to identify cause-effect relationships"""
        
        # Build causal graph from symbols and rules
        causal_graph = self._build_causal_graph(symbols)
        
        # Identify causal chains
        causal_chains = self._find_causal_chains(causal_graph)
        
        reasoning_steps = []
        causal_symbols = []
        
        for chain in causal_chains:
            if len(chain) > 1:  # Valid causal chain
                # Generate causal relationship symbols
                for i in range(len(chain) - 1):
                    causal_symbol = Symbol(
                        name=f"causes({chain[i]}, {chain[i+1]})",
                        symbol_type=SymbolType.RELATION,
                        confidence=self._calculate_causal_strength(chain[i], chain[i+1]),
                        properties={
                            'cause': chain[i],
                            'effect': chain[i+1],
                            'chain_position': i
                        },
                        source='causal_reasoning'
                    )
                    causal_symbols.append(causal_symbol)
                
                reasoning_step = ReasoningStep(
                    step_id=f"causal_step_{len(reasoning_steps)}",
                    reasoning_type=ReasoningType.CAUSAL,
                    input_symbols=symbols,
                    applied_rules=[],
                    output_symbols=[causal_symbol],
                    confidence=causal_symbol.confidence,
                    explanation=f"Identified causal chain: {' → '.join(chain)}"
                )
                
                reasoning_steps.append(reasoning_step)
        
        return symbols + causal_symbols, reasoning_steps
    
    def _build_causal_graph(self, symbols: List[Symbol]) -> Dict[str, List[str]]:
        """Build causal graph from symbols and domain knowledge"""
        
        causal_graph = defaultdict(list)
        
        # Extract causal relationships from rules
        for rule in self.rules.values():
            # Treat rule conditions as potential causes of conclusions
            for condition in rule.conditions:
                for conclusion in rule.conclusions:
                    causal_graph[condition].append(conclusion)
        
        return dict(causal_graph)
    
    def _find_causal_chains(self, causal_graph: Dict[str, List[str]]) -> List[List[str]]:
        """Find causal chains in the graph"""
        
        chains = []
        
        # Simple DFS to find chains
        def dfs(node, current_chain, visited):
            if node in visited:
                return
            
            visited.add(node)
            current_chain.append(node)
            
            if node in causal_graph:
                for neighbor in causal_graph[node]:
                    dfs(neighbor, current_chain.copy(), visited.copy())
            
            if len(current_chain) > 1:
                chains.append(current_chain)
        
        for start_node in causal_graph.keys():
            dfs(start_node, [], set())
        
        return chains
    
    def _calculate_causal_strength(self, cause: str, effect: str) -> float:
        """Calculate strength of causal relationship"""
        
        # Simplified calculation based on rule confidence
        strength = 0.0
        count = 0
        
        for rule in self.rules.values():
            if cause in rule.conditions and effect in rule.conclusions:
                strength += rule.confidence
                count += 1
        
        return strength / count if count > 0 else 0.0
    
    def _calculate_step_confidence(self, applied_rules: List[Rule]) -> float:
        """Calculate confidence for a reasoning step"""
        
        if not applied_rules:
            return 0.0
        
        # Use minimum confidence of applied rules
        return min(rule.confidence for rule in applied_rules)
    
    def _generate_step_explanation(self, 
                                 applied_rules: List[Rule],
                                 derived_symbols: List[Symbol]) -> str:
        """Generate human-readable explanation for reasoning step"""
        
        if not applied_rules:
            return "No rules applied"
        
        explanations = []
        for rule in applied_rules:
            rule_explanation = f"Applied rule {rule.id}: {' AND '.join(rule.conditions)}{' AND '.join(rule.conclusions)}"
            explanations.append(rule_explanation)
        
        symbol_names = [s.name for s in derived_symbols]
        derived_explanation = f"Derived: {', '.join(symbol_names)}"
        
        return "; ".join(explanations) + "; " + derived_explanation

class ExplanationGenerator:
    """Generate comprehensive explanations for neural-symbolic decisions"""
    
    def __init__(self, config: Dict[str, Any]):
        self.config = config
        self.explanation_templates = self._load_explanation_templates()
        
    def _load_explanation_templates(self) -> Dict[str, str]:
        """Load explanation templates"""
        
        return {
            'decision': "The system decided '{decision}' with confidence {confidence:.2f}",
            'neural_evidence': "Neural analysis detected: {concepts} (confidence: {conf:.2f})",
            'symbolic_reasoning': "Symbolic reasoning applied {num_rules} rules over {num_steps} steps",
            'alternative': "Alternative option '{option}' had confidence {confidence:.2f}",
            'uncertainty': "Main uncertainty sources: {sources}"
        }
    
    async def generate_explanation(self, 
                                 decision: str,
                                 symbols: List[Symbol],
                                 reasoning_steps: List[ReasoningStep],
                                 neural_output: Dict[str, torch.Tensor],
                                 alternatives: Optional[List[Dict[str, Any]]] = None) -> Explanation:
        """Generate comprehensive explanation"""
        
        # Calculate overall confidence
        overall_confidence = self._calculate_overall_confidence(symbols, reasoning_steps)
        
        # Generate supporting evidence
        supporting_evidence = self._extract_supporting_evidence(symbols, neural_output)
        
        # Process alternatives
        alternative_decisions = alternatives or []
        
        # Identify uncertainty sources
        uncertainty_sources = self._identify_uncertainty_sources(symbols, reasoning_steps, neural_output)
        
        explanation = Explanation(
            decision=decision,
            confidence=overall_confidence,
            reasoning_chain=reasoning_steps,
            supporting_evidence=supporting_evidence,
            alternative_decisions=alternative_decisions,
            uncertainty_sources=uncertainty_sources
        )
        
        return explanation
    
    def _calculate_overall_confidence(self, 
                                    symbols: List[Symbol],
                                    reasoning_steps: List[ReasoningStep]) -> float:
        """Calculate overall confidence in the decision"""
        
        symbol_confidences = [s.confidence for s in symbols if s.confidence > 0]
        step_confidences = [s.confidence for s in reasoning_steps if s.confidence > 0]
        
        all_confidences = symbol_confidences + step_confidences
        
        if not all_confidences:
            return 0.0
        
        # Use weighted average with recency bias
        weights = np.exp(np.linspace(-1, 0, len(all_confidences)))
        weighted_conf = np.average(all_confidences, weights=weights)
        
        return float(weighted_conf)
    
    def _extract_supporting_evidence(self, 
                                   symbols: List[Symbol],
                                   neural_output: Dict[str, torch.Tensor]) -> List[Dict[str, Any]]:
        """Extract supporting evidence for the decision"""
        
        evidence = []
        
        # Neural evidence
        if 'concept_scores' in neural_output:
            concept_scores = neural_output['concept_scores'].cpu().numpy()
            high_confidence_concepts = []
            
            for i, scores in enumerate(concept_scores):
                for j, score in enumerate(scores):
                    if score > 0.7:  # High confidence threshold
                        high_confidence_concepts.append({
                            'concept_index': j,
                            'confidence': float(score)
                        })
            
            if high_confidence_concepts:
                evidence.append({
                    'type': 'neural_concepts',
                    'data': high_confidence_concepts,
                    'description': f"Neural network identified {len(high_confidence_concepts)} high-confidence concepts"
                })
        
        # Symbolic evidence
        high_confidence_symbols = [s for s in symbols if s.confidence > 0.8]
        if high_confidence_symbols:
            evidence.append({
                'type': 'symbolic_concepts',
                'data': [{'name': s.name, 'confidence': s.confidence} for s in high_confidence_symbols],
                'description': f"Symbolic reasoning validated {len(high_confidence_symbols)} high-confidence symbols"
            })
        
        return evidence
    
    def _identify_uncertainty_sources(self, 
                                    symbols: List[Symbol],
                                    reasoning_steps: List[ReasoningStep],
                                    neural_output: Dict[str, torch.Tensor]) -> List[str]:
        """Identify sources of uncertainty in the decision"""
        
        uncertainty_sources = []
        
        # Neural uncertainty
        if 'uncertainty' in neural_output:
            avg_uncertainty = torch.mean(neural_output['uncertainty']).item()
            if avg_uncertainty > 0.3:
                uncertainty_sources.append(f"High neural uncertainty ({avg_uncertainty:.2f})")
        
        # Low confidence symbols
        low_conf_symbols = [s for s in symbols if s.confidence < 0.5]
        if low_conf_symbols:
            uncertainty_sources.append(f"{len(low_conf_symbols)} low-confidence symbols")
        
        # Conflicting reasoning
        reasoning_confidences = [s.confidence for s in reasoning_steps]
        if reasoning_confidences and max(reasoning_confidences) - min(reasoning_confidences) > 0.5:
            uncertainty_sources.append("Conflicting reasoning steps")
        
        # Missing information
        incomplete_patterns = self._detect_incomplete_patterns(symbols)
        if incomplete_patterns:
            uncertainty_sources.append(f"{len(incomplete_patterns)} incomplete reasoning patterns")
        
        return uncertainty_sources
    
    def _detect_incomplete_patterns(self, symbols: List[Symbol]) -> List[str]:
        """Detect incomplete reasoning patterns"""
        
        # Simplified pattern detection
        incomplete = []
        
        # Look for concepts without supporting relations
        concepts = [s for s in symbols if s.symbol_type == SymbolType.CONCEPT]
        relations = [s for s in symbols if s.symbol_type == SymbolType.RELATION]
        
        for concept in concepts:
            # Check if concept has supporting relations
            supporting_relations = [r for r in relations if concept.name in r.name]
            
            if not supporting_relations and concept.confidence > 0.6:
                incomplete.append(f"Unsupported concept: {concept.name}")
        
        return incomplete
    
    async def generate_natural_language_explanation(self, explanation: Explanation) -> str:
        """Generate natural language explanation"""
        
        parts = []
        
        # Main decision
        decision_text = self.explanation_templates['decision'].format(
            decision=explanation.decision,
            confidence=explanation.confidence
        )
        parts.append(decision_text)
        
        # Supporting evidence
        if explanation.supporting_evidence:
            parts.append("This decision is supported by:")
            for evidence in explanation.supporting_evidence:
                parts.append(f"• {evidence['description']}")
        
        # Reasoning process
        if explanation.reasoning_chain:
            parts.append(f"The reasoning process involved {len(explanation.reasoning_chain)} steps:")
            for i, step in enumerate(explanation.reasoning_chain, 1):
                parts.append(f"{i}. {step.explanation} (confidence: {step.confidence:.2f})")
        
        # Alternatives
        if explanation.alternative_decisions:
            parts.append("Alternative options considered:")
            for alt in explanation.alternative_decisions:
                alt_text = self.explanation_templates['alternative'].format(**alt)
                parts.append(f"• {alt_text}")
        
        # Uncertainties
        if explanation.uncertainty_sources:
            uncertainty_text = self.explanation_templates['uncertainty'].format(
                sources=', '.join(explanation.uncertainty_sources)
            )
            parts.append(uncertainty_text)
        
        return '\n'.join(parts)

class ProductionNeuralSymbolicSystem:
    """Complete production neural-symbolic system"""
    
    def __init__(self, config: Dict[str, Any]):
        self.config = config
        
        # Initialize components
        self.neural_module = NeuralPerceptionModule(config['neural'])
        self.grounding_layer = SymbolGroundingLayer(config['grounding'])
        self.reasoning_engine = SymbolicReasoningEngine(config['reasoning'])
        self.explanation_generator = ExplanationGenerator(config['explanation'])
        
        # Performance monitoring
        self.metrics = NeuralSymbolicMetrics()
        
        # Caching for performance
        self.symbol_cache = {}
        self.reasoning_cache = {}
        
    async def process_input(self, 
                          inputs: Dict[str, Any],
                          context: Optional[Dict[str, Any]] = None,
                          reasoning_type: ReasoningType = ReasoningType.DEDUCTIVE) -> Dict[str, Any]:
        """Process input through complete neural-symbolic pipeline"""
        
        start_time = asyncio.get_event_loop().time()
        
        try:
            # Step 1: Neural perception
            neural_inputs = self._prepare_neural_inputs(inputs)
            
            with torch.no_grad():
                neural_output = self.neural_module(neural_inputs)
            
            self.metrics.record_neural_processing_time(
                asyncio.get_event_loop().time() - start_time
            )
            
            # Step 2: Symbol grounding
            grounding_start = asyncio.get_event_loop().time()
            
            symbols = await self.grounding_layer.ground_symbols(neural_output, context)
            
            if context:
                symbols = await self.grounding_layer.enhance_grounding_with_context(
                    symbols, context
                )
            
            self.metrics.record_grounding_time(
                asyncio.get_event_loop().time() - grounding_start
            )
            
            # Step 3: Symbolic reasoning
            reasoning_start = asyncio.get_event_loop().time()
            
            enhanced_symbols, reasoning_steps = await self.reasoning_engine.reason(
                symbols, reasoning_type
            )
            
            self.metrics.record_reasoning_time(
                asyncio.get_event_loop().time() - reasoning_start
            )
            
            # Step 4: Decision making
            decision = self._make_decision(enhanced_symbols, reasoning_steps)
            
            # Step 5: Generate explanation
            explanation = await self.explanation_generator.generate_explanation(
                decision['decision'],
                enhanced_symbols,
                reasoning_steps,
                neural_output,
                decision.get('alternatives')
            )
            
            # Step 6: Generate natural language explanation
            nl_explanation = await self.explanation_generator.generate_natural_language_explanation(
                explanation
            )
            
            total_time = asyncio.get_event_loop().time() - start_time
            self.metrics.record_total_processing_time(total_time)
            
            return {
                'decision': decision['decision'],
                'confidence': explanation.confidence,
                'symbols': [self._symbol_to_dict(s) for s in enhanced_symbols],
                'reasoning_steps': [self._reasoning_step_to_dict(rs) for rs in reasoning_steps],
                'explanation': explanation,
                'natural_language_explanation': nl_explanation,
                'processing_time': total_time,
                'performance_metrics': self.metrics.get_latest_metrics()
            }
            
        except Exception as e:
            self.metrics.record_error(str(e))
            return {
                'error': str(e),
                'decision': None,
                'confidence': 0.0,
                'explanation': None
            }
    
    def _prepare_neural_inputs(self, inputs: Dict[str, Any]) -> Dict[str, torch.Tensor]:
        """Prepare inputs for neural module"""
        
        neural_inputs = {}
        
        if 'text' in inputs:
            # Tokenize text input
            # This would use the actual tokenizer from the neural module
            neural_inputs['text'] = {
                'input_ids': torch.tensor([[1, 2, 3]]),  # Simplified
                'attention_mask': torch.tensor([[1, 1, 1]])
            }
        
        if 'numerical' in inputs:
            neural_inputs['numerical'] = torch.tensor(inputs['numerical'])
        
        if 'image' in inputs:
            # Process image input
            neural_inputs['image'] = torch.tensor(inputs['image'])
        
        return neural_inputs
    
    def _make_decision(self, 
                      symbols: List[Symbol],
                      reasoning_steps: List[ReasoningStep]) -> Dict[str, Any]:
        """Make final decision based on symbols and reasoning"""
        
        # Aggregate evidence for different decision options
        decision_scores = defaultdict(float)
        
        # Score based on symbol confidence
        for symbol in symbols:
            if symbol.symbol_type == SymbolType.CONCEPT:
                decision_scores[symbol.name] += symbol.confidence
        
        # Score based on reasoning chain confidence
        for step in reasoning_steps:
            for symbol in step.output_symbols:
                if symbol.symbol_type == SymbolType.CONCEPT:
                    decision_scores[symbol.name] += step.confidence * 0.8
        
        if not decision_scores:
            return {'decision': 'no_decision', 'alternatives': []}
        
        # Sort decisions by score
        sorted_decisions = sorted(
            decision_scores.items(),
            key=lambda x: x[1],
            reverse=True
        )
        
        best_decision = sorted_decisions[0]
        alternatives = [
            {'option': name, 'confidence': score}
            for name, score in sorted_decisions[1:3]  # Top 2 alternatives
        ]
        
        return {
            'decision': best_decision[0],
            'alternatives': alternatives
        }
    
    def _symbol_to_dict(self, symbol: Symbol) -> Dict[str, Any]:
        """Convert symbol to dictionary representation"""
        
        return {
            'name': symbol.name,
            'type': symbol.symbol_type.value,
            'confidence': symbol.confidence,
            'properties': symbol.properties,
            'relations': symbol.relations,
            'source': symbol.source
        }
    
    def _reasoning_step_to_dict(self, step: ReasoningStep) -> Dict[str, Any]:
        """Convert reasoning step to dictionary representation"""
        
        return {
            'id': step.step_id,
            'type': step.reasoning_type.value,
            'confidence': step.confidence,
            'explanation': step.explanation,
            'input_count': len(step.input_symbols),
            'output_count': len(step.output_symbols),
            'rules_applied': len(step.applied_rules)
        }

class NeuralSymbolicMetrics:
    """Metrics collection for neural-symbolic system"""
    
    def __init__(self):
        self.metrics = {
            'neural_processing_times': [],
            'grounding_times': [],
            'reasoning_times': [],
            'total_processing_times': [],
            'error_count': 0,
            'decision_count': 0
        }
    
    def record_neural_processing_time(self, time: float):
        self.metrics['neural_processing_times'].append(time)
    
    def record_grounding_time(self, time: float):
        self.metrics['grounding_times'].append(time)
    
    def record_reasoning_time(self, time: float):
        self.metrics['reasoning_times'].append(time)
    
    def record_total_processing_time(self, time: float):
        self.metrics['total_processing_times'].append(time)
        self.metrics['decision_count'] += 1
    
    def record_error(self, error: str):
        self.metrics['error_count'] += 1
    
    def get_latest_metrics(self) -> Dict[str, Any]:
        return {
            'avg_neural_time': np.mean(self.metrics['neural_processing_times'][-100:]) if self.metrics['neural_processing_times'] else 0,
            'avg_grounding_time': np.mean(self.metrics['grounding_times'][-100:]) if self.metrics['grounding_times'] else 0,
            'avg_reasoning_time': np.mean(self.metrics['reasoning_times'][-100:]) if self.metrics['reasoning_times'] else 0,
            'avg_total_time': np.mean(self.metrics['total_processing_times'][-100:]) if self.metrics['total_processing_times'] else 0,
            'error_rate': self.metrics['error_count'] / max(1, self.metrics['decision_count']),
            'total_decisions': self.metrics['decision_count']
        }

Conclusion

Neural-symbolic integration represents a powerful approach to building AI systems that combine the pattern recognition capabilities of neural networks with the interpretability and logical rigor of symbolic reasoning. The key benefits for production systems include:

  1. Interpretability: Decisions can be explained through logical reasoning chains
  2. Reliability: Symbolic constraints ensure logical consistency
  3. Adaptability: Neural components can learn from data while symbolic components encode domain knowledge
  4. Robustness: Multiple reasoning strategies provide fallback mechanisms
  5. Trust: Transparent decision-making process builds user confidence

The implementation presented here provides a foundation for building production-ready neural-symbolic systems that can meet enterprise requirements for reliability, interpretability, and performance. As the field continues to evolve, expect to see further innovations in differentiable programming, probabilistic symbolic reasoning, and hybrid learning algorithms that blur the boundaries between neural and symbolic approaches.

Success with neural-symbolic integration requires careful consideration of the trade-offs between interpretability and performance, as well as domain-specific customization of reasoning strategies and explanation generation. Organizations that invest in these hybrid approaches will be better positioned to deploy AI systems that users can understand, trust, and effectively collaborate with.