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    A Generalisation of Epistemic Splitting Property
    (Springer International Publishing Ag, 2025) Su, Ezgi Iraz
    Answer-set programming (ASP) is a declarative logic programming paradigm that provides an efficient problem-solving approach in logic-based artificial intelligence (AI). While it has proven successful, ASP encounters specific situations where its language falls short of accurately representing and reasoning about incomplete information. Researchers now widely agree that ASP requires powerful introspective reasoning with the use of epistemic modal operators; yet, despite long-lasting debates on how to extend ASP with such operators, they cannot reach a consensus on satisfactory semantics. Cabalar et al. argue that such research should be grounded in formal robustness. Thus, inspired by ASP's foundational properties, they introduce a structural principle called epistemic splitting and designate it as one of the compulsory criteria for epistemic ASP. This paper generalises their approach to a more comprehensive, meticulous, and conservative extension of ASP-splitting, thereby enhancing its applicability and efficiency.
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    Pearce's Characterisation in an Epistemic Domain
    (Open Publishing Association, 2025) Su, Ezgi Iraz
    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 general-purpose nonmonotonic reasoning formalism, based on a monotonic logic called here-and-there logic. EL was basically proposed by Pearce as a foundational framework of ASP. Epistemic specifications (ES) are extensions of ASP-programs with subjective literals. These new modal constructs in the ASP-language make it possible to check whether a regular literal of ASP is true in every (or some) answer-set of a program. ES-programs are interpreted by world-views, which are essentially collections of answer-sets. (Reflexive) autoepistemic logic is a nonmonotonic formalism, modeling self-belief (knowledge) of ideally rational agents. A relatively new semantics for ES is based on a combination of EL and (reflexive) autoepistemic logic. In this paper, we first propose an overarching framework in the epistemic ASP domain. We then establish a correspondence between existing (reflexive) (auto)epistemic equilibrium logics and our easily-adaptable comprehensive framework, building on Pearce's characterisation of answer-sets as equilibrium models. We achieve this by extending Ferraris' work on answer sets for propositional theories to the epistemic case and reveal the relationship between some ES-semantic proposals. © 2025 Open Publishing Association. All rights reserved.
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    Refining the Semantics of Epistemic Specifications
    (Open Publ Assoc, 2021) Su, Ezgi Iraz
    Answer set programming (ASP) is a problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementa-tions in many different fields. However, although researchers acknowledged long ago the necessity of epistemic operators in the language of ASP for better introspective reasoning, this research venue did not attract much attention until recently. Moreover, the existing epistemic extensions of ASP in the literature are not widely approved either, due to the fact that some propose unintended results even for some simple acyclic epistemic programs, new unexpected results may possibly be found, and more importantly, researchers have different reasonings for some critical programs. To that end, Cabalar et al. have recently identified some structural properties of epistemic programs to formally support a possible semantics proposal of such programs and standardise their results. Nonetheless, the soundness of these properties is still under debate, and they are not widely accepted either by the ASP community. Thus, it seems that there is still time to really understand the paradigm, have a mature formalism, and determine the principles providing formal justification of their understand-able models. In this paper, we mainly focus on the existing semantics approaches, the criteria that a satisfactory semantics is supposed to satisfy, and the ways to improve them. We also extend some well-known propositions of here-and-there logic (HT) into epistemic HT so as to reveal the real be-haviour of programs. Finally, we propose a slightly novel semantics for epistemic ASP, which can be considered as a reflexive extension of Cabalar et al.'s recent formalism called autoepistemic ASP.
  • Küçük Resim
    Öğe
    Splitting Property for Epistemic Equilibrium Logics
    (Springer Basel Ag, 2025) Su, Ezgi Iraz
    Answer-set programming (ASP) is a declarative logic programming paradigm that provides an efficient problem-solving approach in logic-based artificial intelligence. In ASP, problems are represented as logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism based on a monotonic logic called here-and-there logic (HT). HT is a three-valued intermediate logic that lies strictly between intuitionistic logic and classical logic. EL was originally proposed as a foundational framework of ASP, where answer sets of an ASP program are captured by the equilibrium models of the corresponding HT theory. While ASP has proven successful as a knowledge-representation formalism, it encounters specific situations where its language falls short of accurately representing and reasoning about incomplete information. Researchers now widely agree that ASP requires powerful introspective reasoning with the use of epistemic modal operators. Therefore, epistemic specifications (ES) have been proposed as extensions of ASP programs with subjective literals. These new modal constructs in the ASP language make it possible to check whether a regular literal of ASP is true in every (or some) answer set of a logic program, which is required to model incomplete information in ASP. Thus, ES programs are interpreted by world-view structures, which are essentially collections of answer sets (or equilibrium models). However, despite long-lasting debates on how to capture the intended meaning of ES programs via world views, researchers have not reached a consensus on fully satisfactory semantics. Recently, Cabalar et al. have argued that such research on ES semantics should be grounded in formal robustness rather than in test examples. Thus, inspired by ASP's foundational properties, they introduced a new structural principle called the epistemic splitting property (E-SP) and designated it as one of the compulsory criteria for epistemic ASP. However, this criterion has left several intuitive semantic approaches unsatisfactory. This paper generalises Cabalar et al.'s approach to a more comprehensive, meticulous, and conservative extension of ASP's original splitting property, thereby broadening the applicability and enhancing the efficiency of epistemic splitting property for general epistemic equilibrium logics.