Logic and Foundations of Mathematics Commons^™

The Proscriptive Principle And Logics Of Analytic Implication, Thomas M. Ferguson

Dissertations, Theses, and Capstone Projects

The analogy between inference and mereological containment goes at least back to Aristotle, whose discussion in the Prior Analytics motivates the validity of the syllogism by way of talk of parts and wholes. On this picture, the application of syllogistic is merely the analysis of concepts, a term that presupposes—through the root ἀνά + λύω —a mereological background.

In the 1930s, such considerations led William T. Parry to attempt to codify this notion of logical containment in his system of analytic implication AI. Parry’s original system AI was later expanded to the system PAI. The hallmark of Parry’s systems—and of …

Self-Referentiality In Constructive Semantics Of Intuitionistic And Modal Logics, Junhua Yu

Dissertations, Theses, and Capstone Projects

This thesis explores self-referentiality in the framework of justification logic. In this framework initialed by Artemov, the language has formulas of the form t:F, which means "the term t is a justification of the formula F." Moreover, terms can occur inside formulas and hence it is legal to have t:F(t), which means "the term t is a justification of the formula F about t itself." Expressions like this is not only interesting in the semantics of justification logic, but also, as we will see, necessary in applications of justification logic in formalizing constructive contents implicitly carried by modal and intuitionistic …