Studies in Universal Logic

By: Razvan Diaconescu

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Paperback | 16 May 2008

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392 Pages

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24.13 x 17.15 x 2.54

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A model theory that is independent of any concrete logical system allows a general handling of a large variety of logics. This generality can be achieved by applying the theory of institutions that provides a precise mathematical formulation for the intuitive concept of a logical system. Especially in computer science, where the development of a huge number of specification logics is observable, institution-independent model theory simplifies and sometimes even enables a concise model-theoretic analysis of the system. Besides incorporating important methods and concepts from conventional model theory, the proposed top-down methodology allows for a structurally clean understanding of model-theoretic phenomena. As a consequence, results from conventional concrete model theory can be understood more easily, and sometimes even new results are obtained.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Computing & I.T.Computer Science Algebra Philosophy Philosophy & Logic

Introduction	p. 1
Categories	p. 7
Basic Concepts	p. 7
Limits and Co-limits	p. 11
Adjunctions	p. 16
2-categories	p. 18
Indexed Categories and Fibrations	p. 20
Institutions	p. 23
From concrete logic to Institutions	p. 23
Examples of institutions	p. 28
Morphisms and Comorphisms	p. 38
Institutions as Functors	p. 45
Theories and Models	p. 49
Theories and Presentations	p. 50
Theory (co-)limits	p. 57
Model Amalgamation	p. 60
The method of Diagrams	p. 65
Inclusion Systems	p. 74
Free Models	p. 82
Internal Logic	p. 91
Logical Connectives	p. 92
Quantifiers	p. 94
Substitutions	p. 97
Representable Signature Morphisms	p. 102
Satisfaction by Injectivity	p. 107
Elementary Homomorphisms	p. 114
Model Ultraproducts	p. 121
Filtered Products	p. 121
Fundamental Theorem	p. 124
Los Institutions	p. 132
Compactness	p. 134
Finitely Sized Models	p. 137
Saturated Models	p. 141
Elementary Co-limits	p. 141
Existence of Saturated Models	p. 144
Uniqueness of Saturated Models	p. 152
Saturated Ultraproducts	p. 157
Preservation and Axiomatizability	p. 163
Preservation by Saturation	p. 163
Axiomatizability by Ultraproducts	p. 168
Quasi-varieties and Initial Models	p. 170
Quasi-Variety Theorem	p. 174
Birkhoff Variety Theorem	p. 178
General Birkhoff Axiomatizability	p. 181
Interpolation	p. 189
Semantic interpolation	p. 192
Interpolation by Axiomatizability	p. 197
Interpolation by Consistency	p. 204
Craig-Robinson Interpolation	p. 211
Borrowing Interpolation	p. 215
Definability	p. 223
Explicit implies implicit definability	p. 226
Definability by Interpolation	p. 228
Definability by Axiomatizability	p. 230
Possible Worlds	p. 235
Internal Modal Logic	p. 236
Ultraproducts of Kripke models	p. 242
Grothendieck Institutions	p. 253
Fibred and Grothendieck Institutions	p. 254
Theory Co-limits and Model Amalgamation	p. 260
Interpolation	p. 267
Institutions with Proofs	p. 275
Free Proof Systems	p. 278
Compactness	p. 284
Proof-theoretic Internal Logic	p. 288
The Entailment Institution	p. 297
Birkhoff Completeness	p. 302
Specification	p. 317
Structured Specifications	p. 318
Specifications with Proofs	p. 327
Predefined Types	p. 331
Logic Programming	p. 337
Herbrand Theorems	p. 338
Unification	p. 340
Modularization	p. 344
Constraints	p. 346
Table of Notation	p. 351
Bibliography	p. 355
Index	p. 368
Table of Contents provided by Ingram. All Rights Reserved.

Studies in Universal Logic

At a Glance

New Edition

Paperback

Shipping

How to return your order

Defective items

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