In this paper, logics are conceived as two-sorted rst-order structures, and we argue that this broad de nition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, syntactical structure, and internal transformations.

. We investigate the notion of bred tableaux which naturally arises from the idea of bred semantics. Dierent implication operators peacefully cohabit and co-operate within the same labelled tableau method. 1 Introduction The last decade has seen a proliferation of dierent logical systems proposed for a variety of dierent purposes, both theoretical and practical. These logics appear to satisfy the needs of dierent application areas or to capture dierent interpretations of the logical operators. This is particularly apparent in the case of the conditional operator. All the dierent implication logics which have been proposed in the literature seem to succeed in modelling some aspect of the ordinary use of this operator, or in suggesting useful non-standard interpretations. What emerges from these developments is a class of operators bearing a family resemblance to each other, each of which may t a dierent application. So, a crucial problem, both in pure and applied logic, is th...

In two earlier papers, the concept of "free amalgamation" has been introduced as a general methodology for interweaving solution structures for symbolic constraints, and it was shown how constraint solvers for two components can be lifted to a constraint solver for the free amalgam. Here we discuss a second general way for combining solution domains, called rational amalgamation. In praxis, rational amalgamation seems to be the preferred combination principle if the two solution structures to be combined are "rational" or "non-wellfounded" domains. It represents, e.g., the way how rational trees and rational lists are interwoven in the solution domain of Prolog III, and a variant has been used by W. Rounds for combining feature structures and hereditarily finite non-wellfounded sets. We show that rational amalgamation is a general combination principle, applicable to a large class of structures. As in the case of free amalgamation, constraint solvers for two component structures can be combined to a constraint solver for their rational amalgam. From this algorithmic point of view, rational amalgamation seems to be interesting since the combination technique for rational amalgamation avoids one source of non-determinism that is needed in the corresponding scheme for free amalgamation.

this paper we shall, instead, use a fragment of this family of logics as a case-study to illustrate a set of methods originating in the LDS program. In particular, we aim to illuminate the following aspects: (I) By virtue of the extra power of labels and labelling algebras, traditional proof systems can be transformed so as to become applicable over a much wider territory whilst retaining a uniform structure. Different logics can be obtained by defining different labelling algebras, which therefore act as "parameters", and the transition from one logic to another can be captured as a parameter-changing process which leaves the structure of deductions unchanged

In a recent paper, Baader and Schulz presented a general method for the combination of constraint systems for purely positive constraints. But negation plays an important role in constraint solving. E.g., it is vital for constraint entailment. Therefore it is of interest to extend their results to the combination of constraint problems containing negative constraints. We show that the combined solution domain introduced by Baader and Schulz is a domain in which one can solve positive and negative "mixed" constraints by presenting an algorithm that reduces solvability of positive and negative "mixed" constraints to solvability of pure constraints in the components. The existential theory in the combined solution domain is decidable if solvability of literals with so-called linear constant restrictions is decidable in the components. We also give a criterion for ground solvability of mixed constraints in the combined solution domain. The handling of negative constraints can be signific...