Related papers: Each normal logic program has a 2-valued Minimal H…
Empirical research in Natural Language Processing (NLP) has adopted a narrow set of principles for assessing hypotheses, relying mainly on p-value computation, which suffers from several known issues. While alternative proposals have been…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
We address the problem of integrating information coming from different sources. The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, i.e. a logic program, and (b) a…
This paper presents a logic framework for modeling the interaction among deductive databases in a P2P (Peer to Peer) environment. Each peer joining a P2P system provides or imports data from its neighbors by using a set of mapping rules,…
This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL…
This technical report describes a new prototype architecture designed to integrate top-down and bottom-up analysis of non-standard linguistic input, where a semantic model of the context of an utterance is used to guide the analysis of the…
Despite great performance on Olympiad-level reasoning problems, frontier large language models can still struggle on high school math when presented with novel problems outside standard benchmarks. Going beyond final accuracy, we propose a…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
This paper provides a model to analyze and identify a decision maker's (DM's) hypothetical reasoning. Using this model, I show that a DM's propensity to engage in hypothetical thinking is captured exactly by her ability to recognize…
The grammatical knowledge of language models (LMs) is often measured using a benchmark of linguistic minimal pairs, where the LMs are presented with a pair of acceptable and unacceptable sentences and required to judge which is more…
Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python…
The logical semantics of normal logic programs has traditionally been based on the notions of Clark's completion and two-valued or three-valued canonical models, including supported, stable, regular, and well-founded models. Two-valued…
Word embedding algorithms produce very reliable feature representations of words that are used by neural network models across a constantly growing multitude of NLP tasks. As such, it is imperative for NLP practitioners to understand how…
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…
Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial…
Abductive reasoning aims to find plausible explanations for an event. This style of reasoning is critical for commonsense tasks where there are often multiple plausible explanations. Existing approaches for abductive reasoning in natural…
Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…
Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…