Related papers: Two Forms of One Useful Logic: Existential Fixed P…
Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
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…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
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…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced…
Datalog^E is the extension of Datalog with existential quantification. While its high expressive power, underpinned by a simple syntax and the support for full recursion, renders it particularly suitable for modern applications on knowledge…
A logic formalism is presented which increases the expressive power of the ID/LP format of GPSG by enlarging the inventory of ordering relations and extending the domain of their application to non-siblings. This allows a concise, modular…
We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a…
We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is…
Temporal epistemic logic is a well-established framework for expressing agents knowledge and how it evolves over time. Within language-based security these are central issues, for instance in the context of declassification. We propose to…
Primal logic arose in access control; it has a remarkably efficient (linear time) decision procedure for its entailment problem. But primal logic is a general logic of information. In the realm of arbitrary items of information (infons),…
Datalog is a popular logic programming language for deductive reasoning tasks in a wide array of applications, including business analytics, program analysis, and ontological reasoning. However, Datalog's restriction to flat facts over…
In this paper we define and study a multi-agent extension of autoepistemic logic (AEL) called distributed autoepistemic logic (dAEL). We define the semantics of dAEL using approximation fixpoint theory, an abstract algebraic framework that…
The frame-based knowledge representation model adopted in IDHS (Intelligent Dictionary Help System) is described in this paper. It is used to represent the lexical knowledge acquired automatically from a conventional dictionary. Moreover,…
The connections among natural language processing and argumentation theory are becoming stronger in the latest years, with a growing amount of works going in this direction, in different scenarios and applying heterogeneous techniques. In…