Computational Logic and Proof Theory: Third Kurt Gödel Colloquium, KGC’93 Brno, Czech Republic, August 24–27, 1993 Proceedings

Egon Börger, Dean Rosenzweig (auth.), Georg Gottlob, Alexander Leitsch, Daniele Mundici (eds.)3540571841, 9783540571841

The Third Kurt G|del Symposium, KGC’93, held in Brno, Czech Republic, August1993, is the third in a series of biennial symposia on logic, theoretical computer science, and philosophy of mathematics. The aim of this meeting wasto bring together researchers working in the fields of computational logic and proof theory. While proof theory traditionally is a discipline of mathematical logic, the central activity in computational logic can be foundin computer science. In both disciplines methods were invented which arecrucial to one another. This volume contains the proceedings of the symposium. It contains contributions by 36 authors from 10 different countries. In addition to 10 invited papers there are 26 contributed papers selected from over 50 submissions.

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Table of contents :
The mathematics of set predicates in Prolog….Pages 1-13
Some connections between set theory and computer science….Pages 14-22
Gödel’s Dialectica interpretation and its two-way stretch….Pages 23-40
Epistemic entrenchment and arithmetical hierarchy (abstract)….Pages 41-42
A critical reexamination of default logic, autoepistemic logic, and only knowing….Pages 43-60
Complexity issues in nonmonotonic logic and logic programming (abstract)….Pages 61-61
Strategies for resolution method in non-classical logics (Abstract)….Pages 62-62
Undecidability of implication problems in logic programming, database theory and classical logic….Pages 63-68
Building up a tool-box for Martin-Löf’s type theory (abstract)….Pages 69-70
The logic of the Gödel proof predicate….Pages 71-82
Superposition with simplification as a decision procedure for the monadic class with equality….Pages 83-96
Computation with access to the reals, but using only classical machines….Pages 97-107
The even more liberalized δ-rule in free variable Semantic Tableaux….Pages 108-119
Differentiating assumptions from extra-logical axioms in natural deduction….Pages 120-131
The inverse of fitting’s functional….Pages 132-143
On loop detection in connection calculi….Pages 144-151
On Arnol’d’s Hilbert symposium problems….Pages 152-158
The structure of exponentials: Uncovering the dynamics of linear logic proofs….Pages 159-171
On different concepts of function introduction….Pages 172-183
Double exponential inseparability of Robinson subsystem Q + from the unsatisfiable sentences in the language of addition….Pages 184-186
On the meaning of essentially unprovable theorems in the presburger theory of addition….Pages 187-189
A syntactic consistency proof for NaDSet….Pages 190-201
A rule-based algorithm for rigid E-unification….Pages 202-210
A scheme for weakened negative introspection in autoepistemic reasoning….Pages 211-222
On the weakness of sharply bounded polynomial induction….Pages 223-230
On the logic of hypergraphs….Pages 231-242
Recursion theoretic properties of frequency computation and bounded queries (extended abstract)….Pages 243-254
Interpreting true arithmetic in degree structures….Pages 255-262
Classical proofs as programs….Pages 263-276
Completeness of the pool calculus with an open built-in theory….Pages 277-288
On the saturation principle for a linear temporal logic….Pages 289-300
A construction of typed lambda models related to feasible computability….Pages 301-312
Nonmonotonic reasoning is sometimes simpler….Pages 313-324
Self-verifying axiom systems….Pages 325-336
Committed-choice concurrent logic programming in linear logic….Pages 337-348