Showing papers by "David Makinson published in 2022"

Relevance-Sensitive Truth-Trees

Abstract: Our goal is to articulate a clear rationale for relevance-sensitive propositional logic. The method: truth-trees. Familiar decomposition rules for truth-functional connectives, accompanied by novel ones for the for the arrow, together with a recursive rule, generate a set of ‘acceptable’ formulae that properly contains all theorems of the well-known system R and is closed under substitution, conjunction, and detachment. We conjecture that it satisfies the crucial letter-sharing condition.

First-order friendliness

Abstract: In this note we study a counterpart in predicate logic of the notion of logical friendliness, introduced into propositional logic in [15]. The result is a new consequence relation for predicate languages with equality using first-order models. While compactness, interpolation and axiomatizability fail dramatically, several other properties are preserved from the propositional case. Divergence is diminished when the language does not contain equality with its standard interpretation.

Boole's indefinite symbols re-examined

Abstract: We show how one can give a clear formal account of Boole’s notorious “indefinite" (or “auxiliary”) symbols by treating them as variables that range over functions from classes to classes rather than just over classes while, at the same time, following Hailperin’s proposal of binding them existentially.