The paper contributes to the study of belief merging in many-valued logics, taking both a theoretical and implementation approach motivated by applications in real-world scenarios. We focus, in particular, on the Horn fragment of signed logic. On the one hand, a characterization of the class of models of a signed regular Horn formula and a sufficient condition for a signed Horn merging operator to satisfy logical IC-postulates are provided. On the other hand, an implementation of the belief merging process in the signed regular Horn fragment is presented.

How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios.

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś-Tarski and the Chang-Łoś-Suszko preservation theorems follow.

In this article, we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the model-theoretic study of fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts being studied are the Leibniz congruence and the structure-preserving relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable using equality-free atomic formulas and parameters from the model. A reduced structure is the quotient of a model modulo this congruence. On the other hand, the structure-preserving relation between two structures plays the same role that the isomorphism relation plays in classical predicate languages with equality.

Abstract We consider separably closed fields of characteristic p > 0 and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the p-component functions.

In this paper we mainly study preservation theorems for two fragments of the infinitary languagesLκκ, withκregular, without the equality symbol: the universal Horn fragment and the universal strict Horn fragment. In particular, whenκisω, we obtain the corresponding theorems for the first-order case. The universal Horn fragment of first-order logic (with equality) has been extensively studied; for references see [10], [7] and [8]. But the universal Horn fragment without equality, used frequently in logic programming, has received much less attention from the model theoretic point of view. At least to our knowledge, the problem of obtaining preservation results for it has not been studied before by model theorists. In spite of this, in the field of abstract algebraic logic we find a theorem which, properly translated, is a preservation result for the strict universal Horn fragment of infinitary languages without equality which, apart from function symbols, have only a unary relation symbol. This theorem is due to J. Czelakowski; see [5], Theorem 6.1, and [6], Theorem 5.1. A. Torrens [12] also has an unpublished result dealing with matrices of sequent calculi which, properly translated, is a preservation result for the strict universal Horn fragment of a first-order language. And in [2] of W. J. Blok and D. Pigozzi we find Corollary 6.3 which properly translated corresponds to our Corollary 19, but for the case of a first-order language that apart from its function symbols has only oneκ-ary relation symbol, and for strict universal Horn sentences. The study of these results is the basis for the present work. In the last part of the paper, Section 4, we will make these connections clear and obtain some of these results from our theorems. In this way we hope to make clear two things: (1) The field of abstract algebraic logic can be seen, in part, as a disguised study of universal Horn logic without equality and so has an added interest. (2) A general study of universal Horn logic without equality from a model theoretic point of view can be of help in the field of abstract algebraic logic.