Logical and Computational Aspects of

The study of diagnostic, visual, spatial, analogical, and temporal reasoning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of traditional notions of reasoning such as classical logic. Understanding the contribution of modeling practices to discovery and conceptual change in science requires expanding scientific reasoning to include complex forms of creative reasoning that are not always successful and can lead to incorrect solutions. The study of these heuristic ways of reasoning is situated at the crossroads of philosophy, artificial intelligence, cognitive psychology, and logic; that is, at the heart of cognitive science. There are several key ingredients common to the various forms of model-based reasoning. The term 'model' comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations. The models are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. Moreover, in the modeling process, various forms of abstraction are used. Evaluation and adaptation take place in light of structural, causal, and/or functional constraints. Model simulation can be used to produce new states and enable evaluation of behaviors and other factors.

Logical Aspects of Model-Based Reasoning	p. 1
A Case Study of the Design and Implementation of Heterogeneous Reasoning Systems	p. 3
Background	p. 3
Overview	p. 4
Some preliminary definitions	p. 6
A framework for heterogeneous reasoning	p. 9
Defining the notion of recasting for Euler/Venn and FOL	p. 10
The implementation	p. 16
A Logical Approach to the Analysis of Metaphors	p. 21
Introduction	p. 21
The interactionist view as a basis for a metaphor theory	p. 22
Some problems with the basic formulation of the interactionist view	p. 24
The advantages of adaptive logics	p. 27
ALM, an adaptive logic for metaphors	p. 28
Conclusions	p. 35
Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction	p. 39
Aim and survey	p. 40
Why the reconstruction is important	p. 42
Main characteristics of abductive reasoning	p. 44
The general format	p. 47
Introducing the dynamics	p. 48
The logics MA1 and CP1	p. 50
Generalizing to the inconsistent case	p. 56
The logics MA2 and CP2	p. 60
Two examples from the history of astronomy	p. 62
Some alternatives	p. 68
Conclusion	p. 69
Diagrammatic Inference and Graphical Proof	p. 73
Introduction	p. 73
Abstraction markers	p. 75
Notational keys	p. 80
The syntactic effect and reinterpretation	p. 82
A diagrammatic inference scheme	p. 84
Global reinterpretation	p. 89
A Logical Analysis of Graphical Consistency Proofs	p. 93
Introduction	p. 93
Examples	p. 96
Analysis	p. 100
Physical on-site inferences	p. 105
Summary	p. 114
Adaptive Logics for Non-Explanatory and Explanatory Diagnostic Reasoning	p. 117
Introduction	p. 117
Non-explanatory and explanatory diagnosis for faults in systems	p. 118
Adaptive logics	p. 122
An adaptive logic for non-explanatory diagnostic reasoning	p. 124
The dynamic proof theory of D[superscript nexp]	p. 127
An illustration of D[superscript nexp]	p. 129
Formal analysis of weak explanatory diagnostic reasoning	p. 130
Formal analysis of strong explanatory diagnostic reasoning	p. 133
An adaptive logic for explanatory diagnostic reasoning	p. 134
The dynamic proof theory of D[superscript exp]	p. 137
An illustration of D[superscript exp]	p. 139
Model-Guided Proof Planning	p. 143
Introduction	p. 143
Proof planning as a way of reasoning	p. 146
Model-based reasoning	p. 150
Semantic restriction and selection of methods	p. 154
Implementation and initial results	p. 158
Conclusion	p. 160
Degrees of Abductive Boldness	p. 163
Introduction: Cautious inference and bold conjecture	p. 163
Abduction as defeasible inference	p. 165
Merging inference and conjecture	p. 168
Abduction via power relations	p. 173
Scientific Explanation and Modified Semantic Tableaux	p. 181
Introduction	p. 181
Modified semantic tableaux	p. 182
Scientific explanation	p. 184
Conclusions	p. 190
Appendix	p. 191
Computational Aspects of Model-Based Reasoning	p. 199
Computational Discovery of Communicable Knowledge	p. 201
Introduction	p. 201
Paradigms for computational discovery	p. 202
Revising regulatory models in microbiology	p. 206
Revising quantitative models in Earth science	p. 211
Related research on computational discovery	p. 219
Concluding remarks	p. 221
Encoding and Using Domain Knowledge on Population Dynamics for Equation Discovery	p. 227
Introduction	p. 227
Population dynamics modeling	p. 228
Equation discovery	p. 234
The equation discovery system Lagramge 2.0	p. 237
Experiments	p. 239
Discussion	p. 243
The Prolog program for transforming the population dynamics domain knowledge into grammar form	p. 245
Reasoning about Models of Nonlinear Systems	p. 249
Reasoning about nonlinear system identification	p. 250
Automated modeling and scientific discovery	p. 256
Representations for model building	p. 260
Orchestrating reasoning about models	p. 264
Conclusion	p. 268
Model-Based Diagnosis of Dynamic Systems: Systematic Conflict Generation	p. 273
Introduction	p. 273
Consistency-based diagnosis: Reiter's Theory	p. 275
Causal graph	p. 276
Graphical notation	p. 277
Problem formulation	p. 277
Strategy for conflicts calculation and diagnoses generation	p. 278
An approach to systematic conflict generation	p. 279
Potential conflict structure	p. 280
An outline of algorithmic approach	p. 282
Diagnoses calculation - elements of algebraic approach	p. 283
An example	p. 286
Conclusions	p. 289
Modeling Through Human-Computer Interactions and Mathematical Discourse	p. 293
Introducing [open phi]-calculus	p. 295
An experiment in LAW	p. 300
A formal system for [open phi]-calculus	p. 301
Conclusion	p. 308
Combining Strategy and Sub-models for the Objectified Communication of Research Programs	p. 313
Scientific objectification of decision-making	p. 314
Strategy: Superior structure of discrete decisions	p. 317
Embedding of sub-models into the decision-structure	p. 322
Imbedding of intra-individual preferences into the decision model	p. 324
Generating individual problem solutions with the decision model	p. 326
Summary and prospects	p. 328
Subject Index	p. 331
Author Index	p. 337
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Logical and Computational Aspects of Model-Based Reasoning

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