Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of `falsehood' to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.
IRIT University of Toulouse（图卢兹大学IRIT研究所）；CNRS（法国国家科学研究中心）；Universität Potsdam（波茨坦大学）
In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalis…
In this paper we consider Epistemic Logic Programs, which extend Answer Set Programming (ASP) with "epistemic operators" and "epistemic negation", and a recent approach to the semantics of such programs in terms of World Views. We propose some observations on the existence and number of world views. We show how to exploit an extended ASP semantics in order to: (i) provide a characterization of world views, different from existing ones; (ii) query world views and query the whole set of world views.
University of Corunna（拉科鲁尼亚大学）；Universität Potsdam（波茨坦大学）；IRIT（图卢兹计算机科学研究所）；University of Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
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 stable models or in some stable model. As it can be imagined, the associated semantics has proved to be non-trivial, as the truth of the subjective literal may interfere with the set of stable models it is supposed to query. As a consequence, no clear agreement has been reached and different semantic proposals have been made in the literature. Unfortunately, c…
Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations 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 res…
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Vienna University of Technology (TU Wien)（维也纳工业大学）
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 answer set semantics proposed in the literature on how they comply with these intuitions. In this note, we consider these three notions and demonstrate on some examples that they may be too strong in general and may exclude some desired answer sets respectively world views. In conclusion, these properties should not be regarded as mandatory properties that every…
We present an epistemic action theory for tractable epistemic reasoning as an extension to the h-approximation (HPX) theory. In contrast to existing tractable approaches, the theory supports functional fluents and postdictive reasoning with static causal laws. We argue that this combination is particularly synergistic because it allows one not only to perform direct postdiction about the conditions of actions, but also indirect postdiction about the conditions of static causal laws. We show that despite the richer expressiveness, the temporal projection problem remains tractable (polynomial), …
University of Corunna（拉科鲁尼亚大学）；Institut de Recherche en Informatique de Toulouse（图卢兹计算机科学研究所）；CNRS（法国国家科学研究中心）
Dynamic Epistemic Logic (DEL) is a family of multimodal logics that has proved to be very successful for epistemic reasoning in planning tasks. In this logic, the agent's knowledge is captured by modal epistemic operators whereas the system evolution is described in terms of (some subset of) dynamic logic modalities in which actions are usually represented as semantic objects called event models. In this paper, we study a variant of DEL, that wecall DEL[ASP], where actions are syntactically described by using an Answer Set Programming (ASP) representation instead of event models. This represen…
University of Nebraska Omaha（内布拉斯加大学奥马哈分校）；University of Potsdam（波茨坦大学）；Alpen-Adria-Universität Klagenfurt（阿尔卑斯-亚德里亚大学克拉根福分校）；Texas Tech University（得克萨斯理工大学）
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 whether a regular literal is true in every or some stable models of the program, those models, in this context also called \emph{belief sets}, being collected in a set called world view. This allows for representing, within the language, whether some proposition should be understood accordingly to the open or the closed world assumption. Several attempts for …
Space and Naval Warfare Systems Center Atlantic（大西洋空间与海战系统中心）；College of Charleston（查尔斯顿学院）；New Mexico State University（新墨西哥州立大学）
As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic Specifications, which adds modal operators K and M to the language of ASP, is one such extension. We call a program in this language an epistemic logic program (ELP). Solvers have thus far been practical for only the simplest ELPs due to exponential growth of the search space. We describe a solver that is able to solve harder problems better (e.g., without exponentia…
KU Leuven（鲁汶大学）；University of Nebraska at Omaha（内布拉斯加大学奥马哈分校）；University of Kentucky（肯塔基大学）
In Knowledge Representation, it is crucial that knowledge engineers have a good understanding of the formal expressions that they write. What formal expressions state intuitively about the domain of discourse is studied in the theory of the informal semantics of a logic. In this paper we study the informal semantics of Answer Set Programming. The roots of answer set programming lie in the language of Extended Logic Programming, which was introduced initially as an epistemic logic for default and autoepistemic reasoning. In 1999, the seminal papers on answer set programming proposed to use this…
Institute of Mathematics and Statistics, Federal University of Bahia - UFBA（巴伊亚联邦大学数学与统计学院）
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transfo…
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 literal is true in all (or in some of) the stable models of the program, being those models collected in a setcalledworld view. One epistemic program may yield several world views but, under the original G91 semantics, some of them resulted from self-supported derivations. During the last eight years, several alternative approaches have been proposed to get rid …
TU Dortmund University（多特蒙德工业大学）；FernUniversität in Hagen（哈根远程大学）
Delgrande's knowledge level account of forgetting provides a general approach to forgetting syntax elements from sets of formulas with links to many other forgetting operations, in particular, to Boole's variable elimination. On the other hand, marginalisation of epistemic states is a specific approach to actively reduce signatures in more complex semantic frameworks, also aiming at forgetting atoms that is very well known from probability theory. In this paper, we bring these two perspectives of forgetting together by showing that marginalisation can be considered as an extension of Delgrande…
University of Corunna（拉科鲁尼亚大学）；University of Potsdam（波茨坦大学）
We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set Programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the ca…
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual be…
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 doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexit…
Cornell University（康奈尔大学）；University of New South Wales（新南威尔士大学）；Forrester Research（弗雷斯特研究公司）
While there have been many attempts, going back to BAN logic, to base reasoning about security protocols on epistemic notions, they have not been all that successful. Arguably, this has been due to the particular logics chosen. We present a simple logic based on the well-understood modal operators of knowledge, time, and probability, and show that it is able to handle issues that have often been swept under the rug by other approaches, while being flexible enough to capture all the higher- level security notions that appear in BAN logic. Moreover, while still assuming that the knowledge operat…
Epistemic logic with non-standard knowledge operators, especially the "knowing-value" operator, has recently gathered much attention. With the "knowing-value" operator, we can express knowledge of individual variables, but not of the relations between them in general. In this paper, we propose a new operator Kf to express knowledge of the functional dependencies between variables. The semantics of this Kf operator uses a function domain which imposes a constraint on what counts as a functional dependency relation. By adjusting this function domain, different interesting logics arise, and in th…
The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.
Epistemic-aware Vision-Language Foundation Model for Fetal Ultrasound Interpretation
National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University（国家多媒体软件工程技术研究中心，武汉大学计算机学院）；College of Computing and Data Science, Nanyang Technological University（computing and Data Science学院，南洋理工大学）
Epistemic Skills: Reasoning about Knowledge and Oblivion
School of Philosophy, Shanxi University, Taiyuan, Shanxi, China（山西大学哲学学院）；School of Philosophy and Social Development, Shandong University, Jinan, Shandong, China（山东大学哲学与社会发展学院）
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
Japan Advanced Institute of Science and Technology（日本北陆先端科学技术大学院大学）
This paper establishes a dual theory about knowledge and argumentation. Our idea is rooted at both epistemic logic and argumentation theory, and we aim to merge these two fields, not just in a superficial way but to thoroughly disclose the intrinsic relevance between knowledge and argumentation. Specifically, we define epistemic Kripke models and argument Kripke models as a dual pair, and then work out a two-way generation method between these two types of Kripke models. Such generation is rigorously justified by a duality theorem on modal formulae's invariance. We also provide realistic examp…
ENS Rennes（雷恩高等师范学院）；University of Naples “Federico II”（那不勒斯费德里科二世大学）
We study dynamic changes of agents' observational power in logics of knowledge and time. We consider CTL*K, the extension of CTL* with knowledge operators, and enrich it with a new operator that models a change in an agent's way of observing the system. We extend the classic semantics of knowledge for perfect-recall agents to account for changes of observation, and we show that this new operator strictly increases the expressivity of CTL*K. We reduce the model-checking problem for our logic to that for CTL*K, which is known to be decidable. This provides a solution to the model-checking proble…
The TARK conference (Theoretical Aspects of Rationality and Knowledge) is a biannual conference that aims to bring together researchers from a wide variety of fields, including computer science, artificial intelligence, game theory, decision theory, philosophy, logic, linguistics, and cognitive science. Its goal is to further our understanding of interdisciplinary issues involving reasoning about rationality and knowledge. Topics of interest include, but are not limited to, semantic models for knowledge, belief, awareness and uncertainty, bounded rationality and resource-bounded reasoning, com…
