In this paper, we examine and compare De Morgan-, Kleene-, and Booleandisjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we describe normal forms and truth tables for classical fuzzy propositional logic and interval-valued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determining logical eq...

Abstract In this paper we discuss sequent calculi for the propositional fragment of logic HYPE. The HYPE was recently suggested by Leitgeb ( Journal Philosophical Logic 48:305–405, 2019) as a hyperintensional contexts. On one hand introduce simple $$\mathbf{G1}$$ G 1 -s...

Short-circuit evaluation denotes the semantics of propositional connectives in which second argument is evaluated only if first insufficient to determine value expression. Compound statements are from left right. widely used programming, with negation and sequential conjunction disjunction as primitives. We study question laws axiomatise short-circuit evaluation. In MSCL (memorising logic), ato...

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...