Related papers: Combining Fixed-Point Definitions and Game Semanti…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Game semantics allows us to look at basic logical concepts from another side. This approach to logic has a long history, there are plenty of different types of games: provability games, semantic games, etc. And there is an interesting type…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive,…
Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress…
We show how solution concepts in games such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of \emph{knowledge-based programs}. Intuitively, all solution…
We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…
"Natural languages are programming languages for minds." Can we or should we take this slogan seriously? If so, how? Can answers be found by looking at the various "dynamic" treatments of natural language developed over the last decade or…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
We define game semantics for the constructive $\mu$-calculus and prove its equivalence to bi-relational semantics. As an application, we use the game semantics to prove that the $\mu$-calculus collapses to modal logic over the modal logic…
This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no…
This article presents an overview of applications of logic programming, classifying them based on the abstractions and implementations of logic languages that support the applications. The three key abstractions are join, recursion, and…
By paying more attention to semantics-based tool generation, programming language semantics can significantly increase its impact. Ultimately, this may lead to ``Language Design Assistants'' incorporating substantial amounts of semantic…
We define a semantics for first-order logic with generalized quantifiers based on double teams. We also define and investigate a notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator…