scholarly journals An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

2010 ◽  
pp. 384-399 ◽  
Author(s):  
Angelo Brillout ◽  
Daniel Kroening ◽  
Philipp Rümmer ◽  
Thomas Wahl
Keyword(s):  
Sequent Calculus ◽  
Presburger Arithmetic

scholarly journals An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

2011 ◽  
Vol 47 (4) ◽  
pp. 341-367 ◽  
Author(s):  
Angelo Brillout ◽  
Daniel Kroening ◽  
Philipp Rümmer ◽  
Thomas Wahl
Keyword(s):  
Sequent Calculus ◽  
Presburger Arithmetic

scholarly journals Sequent calculus as a compiler intermediate language

2016 ◽  
Vol 51 (9) ◽  
pp. 74-88 ◽  
Author(s):  
Paul Downen ◽  
Luke Maurer ◽  
Zena M. Ariola ◽  
Simon Peyton Jones
Keyword(s):  
Sequent Calculus ◽  
Intermediate Language

scholarly journals Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Classical Propositional Logic ◽  
Tableau System ◽  
Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

scholarly journals On Polymorphic Sessions and Functions

2021 ◽  
Vol 43 (2) ◽  
pp. 1-55
Author(s):  
Bernardo Toninho ◽  
Nobuko Yoshida
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Linear Formulation ◽  
Session Types ◽  
Logical Foundation ◽  
Π Calculus ◽  
Soundness And Completeness ◽  
System F ◽  
Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

scholarly journals Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

2021 ◽  
Vol 102 (2) ◽  
pp. 340-356
Author(s):  
Tristram Bogart ◽  
John Goodrick ◽  
Kevin Woods
Keyword(s):  
Periodic Behavior ◽  
Presburger Arithmetic ◽  
Affine Semigroups

scholarly journals A Sequent Calculus for Subtyping Polymorphic Types

2001 ◽  
Vol 164 (2) ◽  
pp. 345-369 ◽  
Author(s):  
Jerzy Tiuryn
Keyword(s):  
Sequent Calculus

A Sequent Calculus

1994 ◽  
pp. 59-74 ◽  
Author(s):  
H.-D. Ebbinghaus ◽  
J. Flum ◽  
W. Thomas
Keyword(s):  
Sequent Calculus
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