Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multi-adjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved a...

Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. En route to our main result we obtain an elementary, logic-independent characterisation of triangu...

In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Lukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full de...

Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops. As part of an investigation into the metatheory of propositional continuous logic...

In this paper we are dealing with the construction of a fuzzy rule based classifier. A three-step method is proposed based on Lukasiewicz logic for the description of the rules and the fuzzy memberships to construct concise and highly comprehensible fuzzy rules. In our method, a genetic algorithm is applied to evolve the structure of the rules and then a gradient based optimization to fine tune...

In this paper, we investigate the Lukasiewicz’s 4-valued modal logic based on the Aristotele’s modal syllogistic. We present a new interpretation of the set of algebraic truth values by introducing the truth and knowledge orderings similar to those in Belnap’s 4-valued bilattice but by replacing the original Belnap’s negation with the lattice pseudo-complement instead. Based on it, we develop a...

In classical propositional logic over finitely many variables no automorphism has any stochastic property, because the dual space is a finite discrete set. In this paper we show that the situation for the infinite-valued Lukasiewicz logic is radically different, by exhibiting a family of Bernoulli automorphisms over two variables. As dynamical systems, these are piecewiselinear area-preserving ...

A (propositional) logic L is paraconsistent with respect to a negation connective if P; P 6`L Q in case P and Q are two distinct atomic variables. Intuitively (and practically) the logic(s) we use should be paraconsistent (with respect to any unary connective!) on the ground of relevance: why should a \contradiction" concerning P imply something completely unrelated? Nevertheless, the most know...

In the present paper, we introduce topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 −, T 1 −, T 2 (αHausdorff)-, T 3 (α-regular)and T 4 (αnormal)-separation axioms. Furthermore, the R 0− and R 1− separation axioms are studied and their relations with the T 1 − ...

In this paper we study the notion of forcing for Lukasiewicz predicate logic ( L∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for L∀, while for the latter, we study the generic and existentially complete standard models of L∀.