Abstracts Vol. 7-No 3/ 1997
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
Keywords: algebraic domain, effective basis, continuous
operation, epistemic state, information system, deduction.
Journal of Applied Non-Classical Logics
Volume 7- No 3/ 1997