Logical and Extralogical Constants

Logical Constants Across Varying Types

We investigate the notion of "logicality" for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for permutations of individual objects, and respect for Boolean structure. Moreover, we show how such properties are systema...

Logical Constants as Punctuation Marks

This paper presents a proof-theoretical approach to the question "What is a logical constant?" This approach starts with the assumption that logic is the science of formal deductions, and that basic formal deductions are structural deductions, i.e. deductions independent of any constant of the language to which the premises and conclusions belong. Logical constants, on which the remaining forma...

Logic , Reasoning and the Logical Constants

Implicational paradoxes and the meaning of logical constants

We discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. We argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads us to select as a plausible candidate LL, a fragment of linear logic which differs from R in that it rejects both contraction and

Constructions, proofs and the meaning of logical constants

During the last decade both mathematicians and philosophers have been interested in the development of various theories of constructions. The study of these theories has been prompted by at least three sorts of considerations. The first theories were proposed by Kreisel around 1960 as a means of formalizing the intended interpreation for the intuitionistic logical constants as presented in Heyt...