Related papers: Epistemic Foundation of Stable Model Semantics
The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
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…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
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…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
In this paper, we propose a variant of stable model semantics for disjunctive logic programming and deductive databases. The semantics, called minimal founded, generalizes stable model semantics for normal (i.e. non disjunctive) programs…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
In the field of knowledge representation, the considered epistemic states are often based on propositional interpretations, also called worlds. E.g., epistemic states of agents can be modelled by ranking functions or total preorders on…
We propose semantic smoothing, a smoothing method for language models that uses embeddings to share statistical observations across semantically similar contexts. The starting point is a decomposition of log-perplexity that motivates…
This paper examines how a notion of stable explanation developed elsewhere in Defeasible Logic can be expressed in the context of formal argumentation. With this done, we discuss the deontic meaning of this reconstruction and show how to…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
In Knowledge Representation, it is crucial that knowledge engineers have a good understanding of the formal expressions that they write. What formal expressions state intuitively about the domain of discourse is studied in the theory of the…
World Models have emerged as a powerful paradigm for learning compact, predictive representations of environment dynamics, enabling agents to reason, plan, and generalize beyond direct experience. Despite recent interest in World Models,…
The Stratified Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratifiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory.…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…