Logicality and Invariance

Logicality and Invariance

This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski-Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized o...

Set-theoretical Invariance Criteria for Logicality

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L ∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a prop...

Logicality of Conditional Rewrite Systems

A conditional term rewriting system is called logical if it has the same logical strength as the underlying conditional equational system. In this paper we summarize known logicality results and we present new sufficient conditions for logicality of the important class of oriented conditional term rewriting systems.

The Logicality of Abduction, Deduction and Induction

Analyticity and Logicality in Semantic Constraints

Logic is often said to be “formal” in some sense. This is generally taken to mean that logical inferences, and therefore valid logical arguments, are those where the conclusion follows based on the form of the constituent sentences alone. Catarina Dutilh Novaes (2011) and John MacFarlane (2000) cite this notion as one of the ways we can think about the formality of logic. More specifically, thi...