Generalized Explosion Principles: A Semantic Perspective
Sankha S. Basu, Sayantan Roy
TL;DR
The paper develops a semantic analogue of explosive reasoning in logic by leveraging abstract model structures (amst) to define eight explosion principles based on unsatisfiability and finite unsatisfiability. It formalizes sat- and finsat-variants (gECQ-sat, sECQ-sat, spECQ-sat, pfECQ-sat and their finsat counterparts), and characterizes these principles in both normal and non-normal amst settings, including relativized satisfiability via filters and ultrafilters. A central thread is the connection between finitary-ness, compactness, and the explosion principles, with precise implications and counterexamples mapping the landscape of semantic explosion. The work links these semantic principles to prior syntactic notions (BasuRoy2024) and outlines rich directions for future research, such as partial explosion and relativized satisfiability, to broaden the semantic understanding of explosion in universal logic.
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.