We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...

The paper deals with fuzzy logic in the narrow sense of Lukasiewicz style, i.e. a special kind of many-valued logic which is aimed at modeling of vagueness phenomenon. This logic is a generalization of Lukasiewicz logic with many interesting properties (for example, generalization of the deduction and completeness theorems hold in it). Our aim is to prepare the background for the resolution in ...

If logic programs are interpreted over a three-valued logic, then often Kleene’s strong three-valued logic with complete equivalence and Fitting’s associated immediate consequence operator is used. However, in such a logic the least fixed point of the Fitting operator is not necessarily a model for the program under consideration. Moreover, the model intersection property does not hold. In this...

The paper deals with fuzzy logic in narrow sense of Lukasiewicz style, i.e. a special kind of many-valued logic which is aimed at modeling of vagueness phenomenon. This logic is a generalization of Lukasiewicz logic with many interesting properties (for example, generalization of the deduction and completeness theorems hold in it). Our aim is to prepare the background for the resolution in fuzz...

This work describes a methodology to combine logic-based systems and connectionist systems. Our approach uses finite truth valued Lukasiewicz logic, where we take advantage of fact, presented by Castro in [6], what in this type of logics every connective can be define by a neuron in an artificial network having by activation function the identity truncated to zero and one. This allowed the inje...

Lukasiewicz's four-valued modal logic is surveyed and analyzed.

Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Lukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

Various types of semantics games for deductive fuzzy logics, most prominently for Lukasiewicz logic, have been proposed in the literature. These games deviate from Hintikka’s original game for evaluating classical first-order formulas by either introducing an explicit reference to a truth value from the unit interval at each game state (as in [4]) or by generalizing to multisets of formulas to ...