We Will Show Them! Essays in Honour of Dov Gabbay, Volume One
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Goal-Directed Methods for Fuzzy Logics
In this contribution we present uniform goal-directed rules for the implicational fragments of the three main formalizations of fuzzy logic; namely, Łukasiewicz logic Ł, Gödel logic G, and Product logic Π. We begin with a historical overview of the goal-directed methodology, focussing in particular on the pioneering work of Dov Gabbay, then proceed by recalling the fundamental systems of fuzzy ...
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It is known that the condition of irreflexivity cannot be characterized in the same way. Yet, the problem of irreflexivity (i.e. the condition ∀x ∼ xRx) arises naturally in tense logics. All flows of time are required to be irreflexive. Take for example future time, with the future operator FA reading “it will be the case that A”. Its truth table is, in a flow of time (T,<, g), where < is irref...
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