Reasoning about proof and knowledge

TL;DR: In this paper , a modal system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle of ''evidence yields belief'' is satisfied is presented.

TL;DR: A formalization of common knowledge from [Lewitzka 2011] is adopted and interpreted here as access-based common knowledge and compared with recent approaches to intuitionistic knowledge to bring together different concepts in a unifying semantic framework based on Heyting algebra expansions.

TL;DR: It is shown here that the conception of verification incorporated in these systems of intuitionistic epistemic logic based on verification with an arithmetical semantics reflects the BHK interpretation, which can be extended to the notion of verification upon which intuitionistic knowledge is based.

TL;DR: This paper finds the logic LP of propositions and proofs and shows that Godel's provability calculus is nothing but the forgetful projection of LP, which achievesGodel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which resisted formalization since the early 1930s.

TL;DR: To obtain a logic that adequately characterizes metaphysical necessity and possibility requires certain additional axiom and rule schemas, one obtains an axiomatization of the most important modal logic, S5, so named because it is the logic generated by the fifth of the systems in Lewis and Langford's Symbolic Logic.

TL;DR: A general Correspondence Theorem is stated showing that behind each epistemic modal logic, there is a robust system of justifications, which renders a new, evidence-based foundation for epistemic logic.