Logic and Foundations of Mathematics Commons^™

Three Essays In Intuitionistic Epistemology, Tudor Protopopescu

Dissertations, Theses, and Capstone Projects

We present three papers studying knowledge and its logic from an intuitionistic viewpoint.

An Arithmetic Interpretation of Intuitionistic Verification

Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic which reflects the intended BHK semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based. This provides the systems of intuitionistic epistemic logic …

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 …