3 research outputs found
Categorical Accommodation of Graded Fuzzy Topological System, Graded Frame and Fuzzy Topological Space with Graded inclusion
A detailed study of graded frame, graded fuzzy topological system and fuzzy
topological space with graded inclusion is already done in our earlier paper.
The notions of graded fuzzy topological system and fuzzy topological space with
graded inclusion were obtained via fuzzy geometric logic with graded con-
sequence. As an off shoot the notion of graded frame has been developed. This
paper deals with a detailed categorical study of graded frame, graded fuzzy
topological system and fuzzy topological space with graded inclusion and their
interrelation
Logic for approximate entailment in ordered universes of discourse
The Logic of Approximate Entailment (LAE) is a graded counterpart of
classical propositional calculus, where conclusions that are only approximately
correct can be drawn. This is achieved by equipping the underlying set of
possible worlds with a similarity relation. When using this logic in
applications, however, a disadvantage must be accepted; namely, in LAE it is
not possible to combine conclusions in a conjunctive way. In order to overcome
this drawback, we propose in this paper a modification of LAE where, at the
semantic level, the underlying set of worlds is moreover endowed with an order
structure. The chosen framework is designed in view of possible applications
Logic of Approximate Entailment in quasimetric spaces
The logic LAE discussed in this paper is based on an approximate entailment
relation. LAE generalises classical propositional logic to the effect that
conclusions can be drawn with a quantified imprecision. To this end, properties
are modelled by subsets of a distance space and statements are of the form that
one property implies another property within a certain limit of tolerance. We
adopt the conceptual framework defined by E. Ruspini; our work is towards a
contribution to the investigation of suitable logical calculi.
LAE is based on the assumption that the distance function is a quasimetric.
We provide a proof calculus for LAE and we show its soundness and completeness
for finite theories. As our main tool for showing completeness, we use a
representation of proofs by means of weighted directed graphs