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Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…
Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…
One of the long-standing research problems on logic programming is to treat the cut predicate in a logical, high-level way. We argue that this problem can be solved by adopting linear logic and choice-disjunctive goal formulas of the form…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
Distilling explicit chain-of-thought reasoning paths has emerged as an effective method for improving the reasoning abilities of large language models (LLMs) across various tasks. However, when tackling complex tasks that pose significant…
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
In this note, we introduce the notion of support graph to define explanations for any model of a logic program. An explanation is an acyclic support graph that, for each true atom in the model, induces a proof in terms of program rules…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…