In our opinion, the notion of an approximative consistency proof may capture the core of the conception of finitary metamathematical consistency proofs which Hilbert developed in his papers on

proof theory in the 1920s.

The main contribution of this article is the introduction of a

proof theory for CCP, i.

As to the

proof theory, six rules are introduced which allow the derivation of a new diagram from two given ones: the rule of erasure of a diagrammatic object, the rule of erasure of part of an x-sequence, the rule of spreading x' s, the rule of introducing a basic region, the rule of conflicting information, the rule of unification of diagrams.

However, coverage of Avron's "The Semantics and

Proof Theory of Linear Logic" in Theoretical Computer Science, 57 (1988), pp.

Objective: The PAnaMoL project aims at systematising

proof theory for modallogics.

The papers, which include abstracts and references, cover type theory (including a dependent set theory), computational

proof theory (including methods of problem solving in elementary geometry), security (including highly efficient proofs of correctness of computations that preserve secrecy), timed and stochastic systems, verification, constraints, proof complexity, finite model theory, concurrency and process calculi, semantics of programming languages (including the algebraic theory of effects), game semantics (including categorical combinatories for "innocent" strategies), linear logic, and topology and computable mathematics.

For instance, the reader will not find any material on modal predicate logic or on the

proof theory of modal logic.

Recall that the branch of mathematical logic called

Proof Theory is only concerned with validity and varieties of constructivity.

Thinking algorithmically is uniquely important just as is scientific investigation, artistic creativity, or

proof theory in mathematics, they say, yet computational thinking is a distinct form of thought, separate from other academic disciplines.

Thirty-nine papers and four invited talks from the August 2006 symposium report the results of recent research on logics of programs,

proof theory, complexity, concurrency, pushdown systems, model theory, temporal logics, lambda calculus, stochastic systems, verification, and approximations.

The main themes of the 14 tutorials and papers are

proof theory and logical foundations of computer science, set theory, model theory, computability and complexity theory, the history of 20th-century logic, philosophy, and applications of logic to cognitive sciences.