Related papers: Expressiveness of Logic Programs under General Sta…
W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable)…
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
Circumscription and logic programs under the stable model semantics are two well-known nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus…
We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass…
Deep learning models suffer from the problem of semantic discontinuity: small perturbations in the input space tend to cause semantic-level interference to the model output. We argue that the semantic discontinuity results from these…
Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
In this paper we analyze declarative deterministic and non-deterministic semantics for active rules. In particular we consider several (partial) stable model semantics, previously defined for deductive rules, such as well-founded, max…
Functional languages with strong static type systems have beneficial properties to help ensure program correctness and reliability. Surprisingly, their practical significance in applications is low relative to other languages lacking in…
Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP^{fs}). We show that…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…