Sequent Systems for Nondeterministic Propositional Logics without Reflexivity

Kuijer, Louwe B ORCID: 0000-0001-6696-9023 (2013) Sequent Systems for Nondeterministic Propositional Logics without Reflexivity. In: 4th International Workshop on Logic, Rationality, and Interaction (LORI).

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Abstract

In order to deal with ambiguity in statements made in a natural language I introduce nondeterministic semantics for propositional logic with an arbitrary set C of connectives. The semantics are based on the idea that Γ entails if and only if every possible deterministic disambiguation of Γ entails every possible deterministic disambiguation of . I also introduce a cut-free sequent style proof system S<inf>C</inf> that is sound and complete for the given semantics. Finally I show that while the semantics and proof system do not satisfy reflexivity they do allow certain kinds of substitution of equivalents. © 2013 Springer-Verlag.

Item Type:	Conference Item (Unspecified)
Uncontrolled Keywords:	46 Information and Computing Sciences
Depositing User:	Symplectic Admin
Date Deposited:	30 Nov 2018 10:52
Last Modified:	09 Jun 2025 15:11
DOI:	10.1007/978-3-642-40948-6_15
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029215