Related papers: Minimal founded semantics for disjunctive logic pr…
Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
The paper considers the representation of k-valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k-valued logic are investigated. Theorems are proved on the coincidence of reduced and…
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…
First Order Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments. In Team Semantics, it is possible to extend First Order Logic via new types of atoms that describe…
By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently,…
Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set…
We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…
To deal with failures as simply as possible, we propose a new foun- dation for the core (untyped) C, which is based on a new logic called task logic or imperative logic. We then introduce a sequential-disjunctive statement of the form S :…
Non-monotonic logic programming is the basis for a declarative problem solving paradigm known as answer set programming (ASP). Departing from the seminal definition by Gelfond and Lifschitz in 1988 for simple normal logic programs, various…
Disentangling the encodings of neural models is a fundamental aspect for improving interpretability, semantic control and downstream task performance in Natural Language Processing. Currently, most disentanglement methods are unsupervised…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
A distributed logic programming language with support for meta-programming and stream processing offers a variety of interesting research problems, such as: How can a versatile and stable data structure for the indexing of a large number of…
We propose new static word embeddings optimised for sentence semantic representation. We first extract word embeddings from a pre-trained Sentence Transformer, and improve them with sentence-level principal component analysis, followed by…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
Semantic Web knowledge representation standards, and in particular RDF and OWL, often come endowed with a formal semantics which is considered to be of fundamental importance for the field. Reasoning, i.e., the drawing of logical inferences…
Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic…