Related papers: Logic programming: laxness and saturation
Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word…
In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
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…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
We propose a general framework for first-order functional logic programming, supporting lazy functions, non-determinism and polymorphic datatypes whose data constructors obey a set C of equational axioms. On top of a given C, we specify a…
Left-sequential logics provide a means for reasoning about (closed) propositional terms with atomic propositions that may have side effects and that are evaluated sequentially from left to right. Such propositional terms are commonly used…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
\emph{Canonical (logic) programs} (CP) refer to normal logic programs augmented with connective $not\ not$. In this paper we address the question of whether CP are \emph{succinctly incomparable} with \emph{propositional formulas} (PF). Our…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
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…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…