Abstracts Vol. 7-No 3/ 1997

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Considerations on the Logic PFD - Wiebe van der Hoeck
Abstract: We investigate a logic PFD, as introduced in [FA]: ``Modal operators with probabilistic interpretations, I'' (Studia Logica 4, Fattorosi-Barnaba and Amati). In our notation, this logic is enriched with operators P>,r (r in [0,1]) where the intended meaning of P>,r(A) is `the probability of A (at a given world) is strictly greater that r'. We also adopt the semantics of [FA]: a class of `F-restricted probabilistic kripkean models'. We give a completeness proof that essentially differs from that in [FA]: our `peremptory lemma' (a lemma in PFD rather that about it) facilitates the construction of a canonical model for PFD considerably. We show that this construction can be carried out useing only finitary means, and also give a filtration-technique for the intended models. We then define an alternative (in some sense more natural) semantics for the logic, and show some of its properties. Finally, we prove decidability of the logic.

Local Possibilistic Logic - Luca Boldrin, Claudio Sossai
Abstract: Possibilistic states of information are fuzzy sets of possible worlds. They constitute a complete lattice, which can be endowed with a monoidal operation (a t-norm) to produce a quantal. An algebraic semantics is presented which links possibilistic formulae with information states, and gives a natural interpretation of logical connectives as operations on fuzzy sets. Due to the quantal structure of information states, we obtain a system which shares several features with (exponential-free) intuitionistic linear logic. Soundness and completeness are proved, parametrically on the choice of the t-norm operation.
Keywords: Many-Valued Logics, Substructural Logics, Possibility Theory.

Quantifiers, modifiers and qualifiers in fuzzy logic - Mingsheng Ying, Bernadette Bouchon-Meunier
Abstract: In this paper, we propose a formalization of fuzzy logic and obtain some results concerning the composition, exchange and compatibility with propositional connectives of fuzzy quantifiers, modifiers and qualifiers in this setting.
Keywords: fuzzy logic, quantifier, modifier, qualifier.

Knowledge Representation as Domains - Alexei Yu. Muravitsky
Abstract: This is a continuing attempt in a series of papers (Kaluzhny and Muravistsky 1993, Muravistsky 1993, Muravistsky 1996) to show how computer-represented knowledge can be arranged as elements of an effectively represented semantic (or algebraic) domain in the sense of (Gunter and Scott 1990). We present a direct deductive description of the domain, which was defined semantically in (Kaluzhny and Muravistsky 1993), via the Scott's notion of information system. Also, the internal structure of the continuous ampliative operations coordinated with the domain's effective basis is established. Though we always remain in the paradigm of the toleration of contradictory information described in (Belnap 19975, 1976), the approach in question could be extended to include domains for consistency knowledge bases.
Keywords: algebraic domain, effective basis, continuous operation, epistemic state, information system, deduction.

Journal of Applied Non-Classical Logics
Volume 7- No 3/ 1997

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