Related papers: Founded (Auto)Epistemic Equilibrium Logic Satisfie…
Defined by Gelfond in 1991 (G91), epistemic specifications (or programs) are an extension of logic programming under stable models semantics that introducessubjective literals. A subjective literal al-lows checking whether some regular…
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…
In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory. It may be three-valued in the sense that for a…
Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embedding in intuitionistic propositional logic ({\bf IPC}). With…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts,…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
In this paper we propose an extension of Answer Set Programming (ASP), and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL), to deal with partial functions. Although the treatment of equality in QEL…
Large language models exhibit intelligence without genuine epistemic understanding, exposing a key gap: the absence of epistemic architecture. This paper introduces the Structured Cognitive Loop (SCL) as an executable epistemological…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a…
Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…