Related papers: A Logic Programming Framework for Possibilistic Ar…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia…
Large language models (LLMs) have taken the world by storm by making many previously difficult uses of AI feasible. LLMs are controlled via highly expressive textual prompts and return textual answers. Unfortunately, this unstructured text…
Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops. Such definitions give rise to…
Fact-seeking question answering with large language models (LLMs) remains unreliable when answers depend on up-to-date or conflicting information. Although retrieval-augmented and tool-using LLMs reduce hallucinations, they often rely on…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme…
Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class SigmaP2 (= NP^NP). Despite this high expressiveness, there are some…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
The paper studies defeasible reasoning in rule-based systems, in particular about legal norms and contracts. We identify rule modifiers that specify how rules interact and how they can be overridden. We then define rule transformations that…
This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel…
The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language…
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…
On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain concept descriptions involving, e.g., "usually true" concept properties, generalized quantifiers, or exceptions. On the other…
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…