STRICT-WEAK LANGUAGES. An analysis of strict implication∗
نویسندگان
چکیده
Modal languages were originally based on the possible-world approach proposed by Lewis, Carnap and others. In other words, modal languages were originally designed to talk about necessity (the box) and possibility (the diamond). Nowadays, modal languages (and certain natural extensions like dynamic languages, μ-calculus language, . . . ) are viewed as tools for analyzing the properties of Kripke structures. For instance, the box can enjoy different meanings like “after the execution of the program terminates”, “according to my knowledge”, “it is provable in Peano arithmetic”, . . . This explains why in recent decades modal languages have been successfully applied to numerous fields: computer science (e.g., artificial intelligence, program verification, database theory, distributed computing, spatial reasoning), epistemology, pure mathematics, game theory, . . . But, what is a modal language? Let us fix a set Prop of (atomic) propositions and a set Mod of modalities. Then, modal formulas are defined by the rule:
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