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Sample logic
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Abstract
The need for a ‘many-valued logic’ in linguistics has been evident since the 1970s, but there was lack of clarity as to whether it should come from the family of fuzzy logics or from the family of probabilistic logics. In this regard, Fine [14] and Kamp [26] pointed out undesirable effects of fuzzy logic (the failure of idempotency and coherence) which kept two generations of linguists and philosophers at arm’s length. (Another unwanted feature of fuzzy logic is the property of truth functionality.) While probabilistic logic is not fraught by the same problems, its lack of constructiveness, i.e. its inability to compose complex truth degrees from atomic truth degrees, did not make it more attractive to linguists either. In the absence of a clear perspective in ‘many-valued logic’, scholars chose to proliferate ontologies grafted atop the classical bivalent logic: ontologies for truth, individuals, events, situations, possible worlds and degrees. The result has been a collection of incompatible classical logics. In this paper, I present sample logic, in particular its semantics (not its axiomatization). Sample logics is a member of the family of probabilistic logics, which is constructive without being truth functional. More specifically, I integrate all the important linguistic data on which the classical logics are predicated. The concepts of (in)dependency and conditional (in)dependency are the cornerstones of sample logic.
Title: Sample logic
Description:
Abstract
The need for a ‘many-valued logic’ in linguistics has been evident since the 1970s, but there was lack of clarity as to whether it should come from the family of fuzzy logics or from the family of probabilistic logics.
In this regard, Fine [14] and Kamp [26] pointed out undesirable effects of fuzzy logic (the failure of idempotency and coherence) which kept two generations of linguists and philosophers at arm’s length.
(Another unwanted feature of fuzzy logic is the property of truth functionality.
) While probabilistic logic is not fraught by the same problems, its lack of constructiveness, i.
e.
its inability to compose complex truth degrees from atomic truth degrees, did not make it more attractive to linguists either.
In the absence of a clear perspective in ‘many-valued logic’, scholars chose to proliferate ontologies grafted atop the classical bivalent logic: ontologies for truth, individuals, events, situations, possible worlds and degrees.
The result has been a collection of incompatible classical logics.
In this paper, I present sample logic, in particular its semantics (not its axiomatization).
Sample logics is a member of the family of probabilistic logics, which is constructive without being truth functional.
More specifically, I integrate all the important linguistic data on which the classical logics are predicated.
The concepts of (in)dependency and conditional (in)dependency are the cornerstones of sample logic.
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