Related papers: The lexicographic closure as a revision process
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting…
While recent years have witnessed the emergence of various explainable methods in machine learning, to what degree the explanations really represent the reasoning process behind the model prediction -- namely, the faithfulness of…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of…
Chain-of-Thought (CoT) explanations are widely used to interpret how language models solve complex problems, yet it remains unclear whether these step-by-step explanations reflect how the model actually reaches its answer, or merely…
Large language models often struggle to recognize their knowledge limits in closed-book question answering, leading to confident hallucinations. While decomposed prompting is typically used to improve accuracy, we investigate its impact on…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
This paper deals with the revision of partially ordered beliefs. It proposes a semantic representation of epistemic states by partial pre-orders on interpretations and a syntactic representation by partially ordered belief bases. Two…
We investigate classical information deficit: a candidate for measure of classical correlations emerging from thermodynamical approach initiated in [Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of information…
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…
An interval-valued fuzzy answer set programming paradigm is proposed for nonmonotonic reasoning with vague and uncertain information. The set of sub-intervals of $[0,1]$ is considered as truth-space. The intervals are ordered using…
We consider the problem of finding plausible knowledge that is missing from a given ontology, as a generalisation of the well-studied taxonomy expansion task. One line of work treats this task as a Natural Language Inference (NLI) problem,…
The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
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…
In this paper we study the uses and the semantics of non-monotonic negation in probabilistic deductive data bases. Based on the stable semantics for classical logic programming, we introduce the notion of stable formula, functions. We show…