Related papers: Logic and computation as combinatorics
Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controversy. The intuitionist advocates for a strict notion of…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
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…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
It has been argued that computational thinking should precede computer programming in the course of a career in computing. This argument is the basis for the slogan "logic first, syntax later" and the development of many cryptic syntax…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…
While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…