Complexity of Strict Implication

abstract. The aim of the present paper is to analyze the complexity of strict implication (together with falsum, conjunction and disjunction). We prove that Ladner's Theorem remains valid when we restrict the language to the strict implication fragment, and that the same holds for Hemaspaandra's Theorem. As a consequence we have that the validity problem for most standard normal modal logics is the same one than the validity problem for its strict implication fragment. We also prove that the validity problems for Visser's basic propositional logic and Visser's formal propositional logic are PSPACE complete. Finally, a polynomial reduction from most standard normal modal logics into its strict implication fragment is presented. Strict implication is defined in the modal language as 0 1 := (0 1) strict implication, where refers to material implication. Strict implication was already considered by Lewis in the birth of modal logic. Nevertheless, there is almost no c...

• Type: Conference
• Year: 2004
• Where: AIML
• Authors: Félix Bou
• Keywords: AIML 2004, AIML 2008, Strict Implication, Strict Implication Fragment, Validity Problem