The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Based on our earlier work on partial logics and extended logic programs Wag91, Wag94, HJW96], and on the possibilistic logic of DLP94], we deene a compositional possibilistic rst-order logic with two kinds of negation as the logical basis of semi-possibilistic and possibilis-tic logic programs. We show that in the same way as the minimal model semantics of relational databases can be reened to ...

The modelling of the semantics of adjectives is notoriously challenging. We consider this problem in the context of the so called ontology-lexicon interface, which attempts to capture the semantics of words by reference to an ontology in description logics or some other, typically first-order, logical formalism. The use of first order logic (hence also description logics), while effective for n...

It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum pr...

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 structur...

In this paper, a logical theory of the, so called, trichotomous evaluative linguistic expressions (TEv-expressions) is presented. These are frequent expressions of natural language, such as “small, very small, roughly medium, extremely big”, etc. The theory is developed using the formal system of higher-order fuzzy logic, namely the fuzzy type theory (generalization of classical type theory). F...