Results 231 to 240 of about 4,006 (251)

Cut-elimination for a logic with definitions and induction

Theoretical Computer Science, 2000
In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ...
Dale Miller
exaly   +2 more sources

Cut Elimination for Gentzen’s Sequent Calculus with Equality and Logic of Partial Terms

Lecture Notes in Computer Science, 2013
We provide a natural formulation of the sequent calculus with equality and establish the cut elimination theorem. We also briefly comment on its applications to the logic of partial terms, when "existence" is formulated as equality with a (bound ...
Franco Parlamento
exaly   +2 more sources

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A proof of the cut-elimination theorem in simple type theory

Journal of Symbolic Logic, 1973
In [4], I introduced a quasi-Boolean algebra, and showed that in a formal system of simple type theory, from which the cut rule is omitted, wffs form a quasi-Boolean algebra, and that the cut-elimination theorem can be formulated in algebraic language.
openaire   +2 more sources

Cut-elimination theorems for some logics associated with double Stone algebras

International Journal of Approximate Reasoning
Fil: Figallo, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur.
Martín Figallo, Juan Sebastián Slagter
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Applications of the Cut Elimination Theorem to Some Subsystems of Classical Analysis

1970
Publisher Summary This chapter discusses the applications of the cut elimination theorem to some subsystems of classical analysis. The principal result presented in the chapter is a constructive consistency proof for the system (Σ 1 2 -ADC) of second order number theory with the Σ 1 2 axiom of dependent choice. It is shown that every derivation in
openaire   +1 more source

Cut-Elimination Theorem for Higher-Order Classical Logic: An Intuitionistic Proof

1987
It is not difficult to see that usual inductive cut-elimination proof fails for higher-order logics. The cause is that the induction goes to the ruin in the case of quantifier rules in logics with the impredicative comprehension shema. In fact, it follows from one Takeuti’s result, that finite proof of cut-elimination is impossible in this case (see ...
openaire   +1 more source

Cut elimination theorem for the second order arithmetic with the π1 1-comprehension axiom and the ω-rule

2018
Mathematics Technical ...
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A New Calculus for Intuitionistic Strong Löb Logic: Strong Termination and Cut-Elimination, Formalised

Lecture Notes in Computer Science, 2023
Rajeev Gore, Rosalie Iemhoff, Gore Rajeev   +2 more
exaly  

Phase semantic cut-elimination and normalization proofs of first- and higher-order linear logic

Theoretical Computer Science, 1999
Mitsuhiro Okada
exaly  

Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic

Studia Logica, 2019
Norihiro Kamide, Yoni Zohar, Kamide Norihiro   +2 more
exaly