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A Quantified Temporal Logic for Ampliation and Restriction

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Chapter Summary

Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. As all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. As a case study, this chapter looks at the supposition theory of Lambert of Lagny, extracting from it a temporal logic and providing a formalization of that logic. The chapter uses the techniques of modern temporal logic to provide a formal analysis of the future- and past-tensed parts of supposition theory. It starts with definitions of signification and supposition, followed by the standard division of supposition into its types, and concludes with a discussion of appellatio, restrictio, ampliatio, distributio, and relatio.

Keywords: basic propositional logic; medieval theories; natural language; supposition theory; temporal logic



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