A uniform construction for sequent calculi for finite-valued first-order logics with dis- tribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand's theorem for the four-valued knowledge- representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

https://people.ucalgary.ca/~rzach/static/mvlcutel.pdf

Proof Theory

Elimination of cuts in first-order finite-valued logics

This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

Proof Analysis: A Contribution to Hilbert's Last Problem

Proof-theoretic analysis of termination proofs

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

Proof Theory

Citations

Elimination of cuts in first-order finite-valued logics

Proof Analysis: A Contribution to Hilbert's Last Problem

Proof-theoretic analysis of termination proofs

A logic road from special relativity to general relativity

Classes and truths in set theory

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Untersuchungen über das logische Schließen. II

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