Related papers: LPC(ID): A Sequent Calculus Proof System for Propo…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…
This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
We present the logical induction criterion for computable algorithms that assign probabilities to every logical statement in a given formal language, and refine those probabilities over time. The criterion is motivated by a series of stock…
Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This…
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…