Related papers: Abduction in Well-Founded Semantics and Generalize…
We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of…
This study evaluates the GPT-4 Large Language Model's abductive reasoning in complex fields like medical diagnostics, criminology, and cosmology. Using an interactive interview format, the AI assistant demonstrated reliability in generating…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…
We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic…
Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…
Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic…
Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…
Thom Fr\"uhwirth presented a short, elegant and efficient Prolog program for the n queens problem. However the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a…
Thom Fr\"uhwirth presented a short, elegant and efficient Prolog program for the n queens problem. However the program may be seen as rather tricky and one may be not convinced about its correctness. This paper explains the program in a…
This paper contains examples for a companion paper "The Prolog Debugger and Declarative Programming", which discusses (in)adequacy of the Prolog debugger for declarative programming. Logic programming is a declarative programming paradigm.…
Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
Bayesian belief networks can be used to represent and to reason about complex systems with uncertain, incomplete and conflicting information. Belief networks are graphs encoding and quantifying probabilistic dependence and conditional…
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…
Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops…