Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, i.e., contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently. This work is under consideration for acceptance in TPLP.
TU Wien（维也纳工业大学）；University of Potsdam（波茨坦大学）；University of Klagenfurt（克拉根福大学）
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational complexity reaching up to the fourth level of the polynomial hierarchy. However, in contrast to standard ASP, dedicated investigations towards tractability have not been undertaken yet. In this paper, we give first results in this direction and show that central ELP problems can be solved in linear time for ELPs exhibiting structural properties in terms of bounde…
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.
Answer Set Programming (ASP) is a problem modeling and solving framework for several problems in KR with growing industrial applications. Also for studies of computational complexity and deeper insights into the hardness and its sources, ASP has been attracting researchers for many years. These studies resulted in fruitful characterizations in terms of complexity classes, fine-grained insights in form of dichotomy-style results, as well as detailed parameterized complexity landscapes. Recently, this lead to a novel result establishing that for the measure treewidth, which captures structural d…
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…
Epistemic Logic Programs (ELPs) are an extension of Answer Set Programming (ASP) with epistemic operators that allow for a form of meta-reasoning, that is, reasoning over multiple possible worlds. Existing ELP solving approaches generally rely on making multiple calls to an ASP solver in order to evaluate the ELP. However, in this paper, we show that there also exists a direct translation from ELPs into non-ground ASP with bounded arity. The resulting ASP program can thus be solved in a single shot. We then implement this encoding method, using recently proposed techniques to handle large, non…
Space and Naval Warfare Systems Center Atlantic（大西洋太空与海战系统中心）；College of Charleston（查尔斯顿学院）
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective reasoning and enhanced capability, particularly when reasoning with incomplete information. An epistemic logic program is a set of rules in this language. Infused with the research has been the desire for an efficient solver to enable the practical use of such programs for problem solving. In this paper, we report on the current state of development of epistemi…
Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural properties during solving. One of such structural indicators is the so-called treewidth, which tries to measure how close a formula instance is to being easy (tree-like). This work focuses on logic-based problems and treewidth-based methods and tools for solving them. Many of these problems are also relevant for knowledge representation and reasoning (KR) as well…
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…
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…
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…
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 largely used to specify the agent's belief state - whether representing the agent's `explicit beliefs' or as a computational model for her 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 a dynamic epi…
Epistemic Logic Programs: Non-Ground and Counting Complexity
Institute of Logic and Computation, TU Wien（维也纳技术大学逻辑与计算研究所）；Department of Computer and Information Science (IDA), Linköping University（林雪平大学计算机与信息科学系）；Univ. Artois, CNRS, CRIL（阿图瓦大学、法国国家科学研究中心、CRIL研究所）
Universidad Simón Bolívar（西蒙玻利瓦尔大学）；Universidad de Los Andes（德洛斯安第斯大学）
In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that operators are represented by total preorders. This important representation is exploited by Darwiche and Pearl to shift the notion of epistemic state to a more abstract one, where the paradigm of epistemic state is indeed that of a total preorder over interpretations. In this work, we introduce a 3-valued logic where the formulas can be identified with a generalisa…
Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known …
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…
University of Klagenfurt（克拉根福大学）；Czech Technical University in Prague（捷克布拉格技术大学）
In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem …
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 …
A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions
Faculty of Mathematics（数学系）；Computer Science, University of Hagen, 58084 Hagen, Germany（计算机科学，海因斯大学，德国）；Department of Computer Science, Technology Dortmund University, 44221 Dortmund, Germany（计算机科学系，多特蒙德技术大学，德国）
A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification
Institute for AI, Data Analysis and Systems (AIDAS) School of Engineering, Computing and Mathematics, Oxford Brookes University, UK（人工智能、数据分析和系统研究所（AIDAS）工程、计算与数学学院，英国奥克斯福德布鲁克斯大学）
TU Wien（维也纳工业大学）；University of Potsdam（波茨坦大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorit…
Peking University（北京大学）；University of Auckland（奥克兰大学）
In standard epistemic logic, agent names are usually assumed to be common knowledge implicitly. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid. The language can handle various de dicto and de re distinctions in a natural way. The main technical result is a complete axiomatisation of this logic over S5 models.
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…
DTU Compute, Technical University of Denmark（丹麦技术大学DTU计算学院）；London School of Economics（伦敦政治经济学院）；Center for Information and Bubble Studies, University of Copenhagen（哥本哈根大学信息与泡沫研究中心）
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists x\mathsf{blocks\_door}(x)$. In contrast, several recent epistemic planning frameworks are built on propositional epistemic logic. The epistemic language is useful to describe planning problems involving higher-order reasoning or epistemic goals such as $K_{a}\neg\mathsf{problem}$. This paper develops a first-order version of Dynamic Epistemic Logic (DEL). In this framewo…
Dynamic Epistemic Logic (DEL) is a logical framework in which one can describe in great detail how actions are perceived by the agents, and how they affect the world. DEL games were recently introduced as a way to define classes of games with imperfect information where the actions available to the players are described very precisely. This framework makes it possible to define easily, for instance, classes of games where players can only use public actions or public announcements. These games have been studied for reachability objectives, where the aim is to reach a situation satisfying some …
Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962). Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of "knowing that". However, knowledge is expressed in everyday life by using various other locutions such as "knowing whether", "knowing what", "knowing how" and so on (knowing-wh hereafter). Such knowledge expressions are better captured in quantified ep…
Bayreuth University（拜罗伊特大学）；University of Bamberg（班贝格大学）；Lund University（隆德大学）；University of Copenhagen（哥本哈根大学）
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous wi…
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 general schema of $\exists x \Box ϕ$, e.g., knowing how to achieve $ϕ$ roughly means that there exists a way such that you know that it is a way to ensure that $ϕ$. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we propose a very general and powerful framework based on quantifier-free predicate language extended …
Jinan University（暨南大学）；Griffith University（格里菲斯大学）；Guangdong Institute of Public Administration（广东行政学院）
Epistemic logics are a primary formalism for multi-agent systems but major reasoning tasks in such epistemic logics are intractable, which impedes applications of multi-agent epistemic logics in automatic planning. Knowledge compilation provides a promising way of resolving the intractability by identifying expressive fragments of epistemic logics that are tractable for important reasoning tasks such as satisfiability and forgetting. The property of logical separability allows to decompose a formula into some of its subformulas and thus modular algorithms for various reasoning tasks can be dev…
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.
LIX, CNRS（法国国家科学研究中心LIX实验室）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；University of Strathclyde（思克莱德大学）；UNAM（墨西哥国立自治大学）
The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work (Information and Computation, 2021). Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such m…
We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the …
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The paper studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how" strategies. The main technical result is a sound and complete trimodal logical system that describes the properties of this interplay.
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…
Sun Yat-sen University（中山大学）；Qiannan Normal College for Nationalities（黔南民族师范学院）；Peking University（北京大学）；University of Groningen（格罗宁根大学）
In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language.
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…
Institute for Logic, Language and Computation（逻辑、语言与计算研究所）；University of Amsterdam（阿姆斯特丹大学）；Donders Institute for Brain, Cognition, and Behaviour（唐德斯大脑、认知与行为研究所）；Radboud University（拉德堡德大学）
In this paper we introduce a computational-level model of theory of mind (ToM) based on dynamic epistemic logic (DEL), and we analyze its computational complexity. The model is a special case of DEL model checking. We provide a parameterized complexity analysis, considering several aspects of DEL (e.g., number of agents, size of preconditions, etc.) as parameters. We show that model checking for DEL is PSPACE-hard, also when restricted to single-pointed models and S5 relations, thereby solving an open problem in the literature. Our approach is aimed at formalizing current intractability claims…
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 existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The article studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how" strategies. The main technical result is a sound and complete trimodal logical system that describes the properties of this interplay.
Institute for Logic, Language and Computation University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）
Dynamic epistemic logic (DEL) is a logical framework for representing and reasoning about knowledge change for multiple agents. An important computational task in this framework is the model checking problem, which has been shown to be PSPACE-hard even for S5 models and two agents---in the presence of other features, such as multi-pointed models. We answer open questions in the literature about the complexity of this problem in more restricted settings. We provide a detailed complexity analysis of the model checking problem for DEL, where we consider various combinations of restrictions, such …
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.
Centrum Wiskunde & Informatica（荷兰数学与计算机科学中心）；University of Warsaw（华沙大学）；University of Liverpool（利物浦大学）
Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable.…
Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge among economists'. We introduce such a logic of common knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic that we keep generic, with one possible agent logic being ALC. We show that AGEL is EXPTIME-complete, with the lower bound estab…
