Modal Logic With Non-deterministic Semantics: Part I - Propositional Case

Marcelo E. Coniglio; Luis Fariñas del Cerro; Newton M. Peron

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arXiv · 1808.10007

Modal Logic With Non-deterministic Semantics: Part I - Propositional Case

Marcelo E. Coniglio·Luis Fariñas del Cerro·Newton M. Peron

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Abstract

In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and extended his hierarchy, proposing weaker six-valued systems in which the T axiom was replaced by the deontic D axiom. Here, we eliminate both axioms, proposing even weaker systems with eight values. Besides, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those systems. We will show that finite deterministic matrices do not characterize any of them.

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BibTeX RIS

Marcelo E. Coniglio, Luis Fariñas del Cerro, Newton M. Peron. 2018-08-29. Modal Logic With Non-deterministic Semantics: Part I - Propositional Case. https://arxiv.org/abs/1808.10007

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