A Manual of Intensional Logic by Johan van Benthem

By Johan van Benthem

Intensional common sense is the technical examine of such "intensional" phenomena in human reasoning as modality, wisdom, or circulate of time. those all require a richer semantic photograph than typical fact values in a single static setting. any such photograph is equipped by means of so-called "possible worlds semantics," a paradigm that's surveyed during this e-book, either as to its exterior resources of motivation and as to the inner dynamics of the ensuing software. particularly, ^IManual of Intensional Logic^R provides the key "classical" subject matters, together with modal common sense, stressful good judgment, and conditional good judgment, all of which illustrate motivations coming from philosophy and linguistics. The e-book additionally discusses contemporary computational purposes in desktop technological know-how and AI. eventually, ^IManual of Intensional Logic^R takes up contemporary advancements within the examine of language and data making themselves felt within the zone. The booklet examines the function of partial information--with illustrations drawn from assorted branches of Intensional Logic--and a variety of impacts stemming from present theories of the semantics of typical language, regarding generalized quantifiers and theories of varieties.

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Behavior of programs can then be described using so-called preconditions and postconditions, as in the well-known correctness assertion for each state s\ satisfying

The Lewis semantics has some peculiar features, which come out when the above idea is extended to the case of infinite sets of worlds W, In that realm, there need not be "closest" <£>-worlds (there could be ever 28 Conditionals closer worlds where you are taller than you actually are), and the above truth clause requires amendments—none of them wholly satisfactory. This possible diversity of truth definitions (in addition to the diversity in constraints on model classes which we have encountered already) is an interesting semantic phenomenon, challenging the surely not self-evident presupposition of much recent research that unique truth conditions must be forthcoming for linguistic expressions (rather than some "range of explication").

The End of the Syntactical Phase Perhaps the nicest exposition of the syntactic perspective is found in Reseller's paper in the Sosa volume. Our beliefs (theories, prejudices) T come in a hierarchy of statements to be given up, say, in the order of laws/auxiliary hypotheses/facts. The test then becomes: to add A to T, removing statements from T to obtain consistency, starting where it hurts least. Example: // the match had been lighted (L), there would have been an explosion (E). Let us assume a background theory with 26 Conditionals one law: L A O —> E, where O is the auxiliary hypothesis that oxygen was present, together with the facts ->i, ->E.

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