Computational Logic and Proof Theory

The Third Kurt G|del Symposium, KGC'93, held in Brno, CzechRepublic, August1993, is the third in a series of biennialsymposia on logic, theoretical computer science, andphilosophy of mathematics. The aim of this meeting wastobring together researchers working in the fields ofcomputational logic and proof theory. While proof theorytraditionally is a discipline of mathematical logic, thecentral activity in computational logic can be foundincomputer science. In both disciplines methods were inventedwhich arecrucial to one another. This volume contains theproceedings of the symposium. It contains contributions by36 authors from 10 different countries. In addition to 10invited papers there are 26 contributed papers selected fromover 50 submissions.

The mathematics of set predicates in Prolog.- Some connections between set theory and computer science.- Gödel's Dialectica interpretation and its two-way stretch.- Epistemic entrenchment and arithmetical hierarchy (abstract).- A critical reexamination of default logic, autoepistemic logic, and only knowing.- Complexity issues in nonmonotonic logic and logic programming (abstract).- Strategies for resolution method in non-classical logics (Abstract).- Undecidability of implication problems in logic programming, database theory and classical logic.- Building up a tool-box for Martin-Löf's type theory (abstract).- The logic of the Gödel proof predicate.- Superposition with simplification as a decision procedure for the monadic class with equality.- Computation with access to the reals, but using only classical machines.- The even more liberalized ?-rule in free variable Semantic Tableaux.- Differentiating assumptions from extra-logical axioms in natural deduction.- The inverse of fitting's functional.- On loop detection in connection calculi.- On Arnol'd's Hilbert symposium problems.- The structure of exponentials: Uncovering the dynamics of linear logic proofs.- On different concepts of function introduction.- Double exponential inseparability of Robinson subsystem Q+ from the unsatisfiable sentences in the language of addition.- On the meaning of essentially unprovable theorems in the presburger theory of addition.- A syntactic consistency proof for NaDSet.- A rule-based algorithm for rigid E-unification.- A scheme for weakened negative introspection in autoepistemic reasoning.- On the weakness of sharply bounded polynomial induction.- On the logic of hypergraphs.- Recursion theoretic properties of frequency computation and bounded queries (extended abstract).-Interpreting true arithmetic in degree structures.- Classical proofs as programs.- Completeness of the pool calculus with an open built-in theory.- On the saturation principle for a linear temporal logic.- A construction of typed lambda models related to feasible computability.- Nonmonotonic reasoning is sometimes simpler.- Self-verifying axiom systems.- Committed-choice concurrent logic programming in linear logic.