Related papers: Fixpoint 3-valued semantics for autoepistemic logi…
We present an order-theoretical fixed point theorem for increasing multivalued operators suitable for the method of sub-supersolutions and its application to the following multivalued quasi-variational inclusion: Let $\Omega \subset \mathbb…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and…
Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlier work that obtains Hennessy-Milner theorems as corollaries…
The fixpoint completion fix(P) of a normal logic program P is a program transformation such that the stable models of P are exactly the models of the Clark completion of fix(P). This is well-known and was studied by Dung and Kanchanasut…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires…
We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the…
As large language models (LLMs) are increasingly considered for automated assessment and feedback, understanding when LLM marking can be trusted is essential. We evaluate LLM-as-a-judge marking across three physics assessment formats -…
Hybrid Knowledge Bases based on Lifschitz's logic of Minimal Knowledge with Negation as Failure are a successful approach to combine the expressivity of Description Logics and Logic Programming in a single language. Their syntax, defined by…
This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…
Machine learning models provide statistically impressive results which might be individually unreliable. To provide reliability, we propose an Epistemic Classifier (EC) that can provide justification of its belief using support from the…
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…