Related papers: Fibring by functions as a method for combining mat…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
When we represent logical, connective implications by directed edges, the resulting set of directed edges can be regarded as a complex network. In this article, we compose a network model that represents a deductive-logic-like structure…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…