Generalized Explosion Principles: A Semantic Perspective

TL;DR

This paper explores the semantic foundations of explosion principles in logic, analyzing their characterizations and interconnections through abstract model structures and satisfiability concepts.

Contribution

It introduces semantic analogues of explosion principles and studies their characterizations and relationships within abstract model structures.

Findings

Semantic analogues of explosion principles are characterized and interconnected.

The distinction between syntactic and semantic explosion is clarified.

Abstract model structures are used to analyze satisfiability and explosion principles.

Abstract

This article is motivated by the fact that there is a distinction between the descriptions of logical explosion from syntactic and semantic points of view. The discussion is illustrated using the concept of abstract model structures and the notions of satisfiability and finite satisfiability in these structures. Various principles of explosion have been described in terms of unsatisfiability or finite unsatisfiability. The semantic analogues of the principles of explosion introduced in [3] have also been considered among these. The article also studies the characterizations of and the interconnections between these new principles of explosion.