Epistemic Logic Programs Research Articles

Epistemic Logic Programs: A Study of Some Properties

Abstract 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, that is, syntactically, sets of sets of atoms. Different semantic approaches propose different characterizations of world views. Recent work has introduced semantic properties that should be met by any semantics for ELPs, like the Epistemic Splitting Property, that, if satisfied, allows to modularly compute world views in a bottom-up fashion, analogously to “traditional” ASP. We analyze the possibility of changing the perspective, shifting from a bottom-up to a top-down approach to splitting. We propose a basic top-down approach, which we prove to be equivalent to the bottom-up one. We then propose an extended approach, where our new definition: (i) is provably applicable to many of the existing semantics; (ii) operates similarly to “traditional” ASP; (iii) provably coincides under any semantics with the bottom-up notion of splitting at least on the class of Epistemically Stratified Programs (which are, intuitively, those where the use of epistemic operators is stratified); (iv) better adheres to common ASP programming methodology.

Evaluating Epistemic Logic Programs via Answer Set Programming with Quantifiers

In this paper we introduce a simple way to evaluate epistemic logic programs by means of answer set programming with quantifiers, a recently proposed extension of answer set programming. The method can easily be adapted for most of the many semantics that were proposed for epistemic logic programs. We evaluate the proposed transformation on existing benchmarks using a recently proposed solver for answer set programming with quantifiers, which relies on QBF solvers.

Thirty years of Epistemic Specifications

AbstractThe 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 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 capturing the intuitions underlying the language by means of a formal semantics were given, resulting in a multitude of proposals that makes it difficult to understand the current state of the art. In this article, we provide an overview of the inception of the field and the knowledge representation and reasoning tasks it is suitable for. We also provide a detailed analysis of properties of proposed semantics, and an outlook of challenges to be tackled by future research in the area.

Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

AbstractExtending the popular answer set programming 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, that is, 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.

Eclingo : A Solver for Epistemic Logic Programs

AbstractWe 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 cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo ’s efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results.

Structural Decompositions of Epistemic Logic Programs

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 bounded treewidth. We also provide a full dynamic programming algorithm that adheres to these bounds. Finally, we show that applying treewidth to a novel dependency structure—given in terms of epistemic literals—allows to bound the number of ASP solver calls in typical ELP solving procedures.

Epistemic Logic Programs: A Different World View

Epistemic Logic Programs (ELPs), an extension of Answer Set Programming (ASP) with epistemic operators, have received renewed attention from the research community in recent years. Classically, evaluating an ELP yields a set of world views, with each being a set of answer sets. In this paper, we propose an alternative definition of world views that represents them as three-valued assignments, where each atom can be either always true, always false, or neither. Based on several examples, we show that this definition is natural and intuitive. We also investigate relevant computational properties of these new semantics, and explore how other notions, like strong equivalence, are affected.

About Epistemic Negation and World Views in Epistemic Logic Programs

AbstractIn 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 ofWorld 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.

Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

AbstractIn 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 ofepistemic splittingprovides 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 formalised as a property of epistemic semantics calledfoundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-calledFounded Autoepistemic Equilibrium Logic(FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we calledFounded Epistemic Equilibrium Logic(FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.

On Uniform Equivalence of Epistemic Logic Programs

AbstractEpistemic 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 as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

Strong Equivalence for Epistemic Logic Programs Made Easy

Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important question is under which conditions a sub-program can be replaced by another one without changing the meaning, in any context. This problem is known as strong equivalence, and is well-studied for ASP. For ELPs, this question has been approached by embedding them into epistemic extensions of equilibrium logics. In this paper, we consider a simpler, more direct characterization that is directly applicable to the language used in state-of-the-art ELP solvers. This also allows us to give tight complexity bounds, showing that strong equivalence for ELPs remains coNP-complete, as for ASP. We further use our results to provide syntactic characterizations for tautological rules and rule subsumption for ELPs.

A parallel memory-efficient epistemic logic program solver: harder, better, faster

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, at the time of its development (mid-2016), was able to solve harder problems better (e.g., without exponentially-growing memory needs w.r.t. K and M occurrences) and faster than any other known ELP solver.

The language of epistemic specifications (refined) including a prototype solver

Abstract In this article, we present a new version of the language of Epistemic Specifications. The goal is to simplify and improve the intuitive and formal semantics of the language. We describe an algorithm for computing solutions of programs written in this new version of the language. The new semantics is illustrated by a number of examples, including an Epistemic Specifications-based framework for conformant planning. In addition, we introduce the notion of an epistemic logic program with sorts . This extends recent efforts to define a logic programming language that includes the means for explicitly specifying the domains of predicate parameters. An algorithm and its implementation as a solver for epistemic logic programs with sorts is also discussed.

Ell Secure Information System Using Modal Logic Technique

In this paper, the authors propose a formal logic technique to protect information systems. As the widespread use of computer systems grows, the security of the information stored in such systems has become more important. As a security mechanism, authorization or access control ensures that all accesses to the system resources occur exclusively according to the access polices and rules specified by the system security agent. Authorization specification has been widely studied and a variety of approaches have been investigated. The authors propose a formal language with modal logic to specify the system security policies. The authors also provide the reasoning in response to system access requests, especially in situations where the security agent’s knowledge base is incomplete. The semantics of this language is provided by translating it into epistemic logic program in which knowledge related modal operators are employed to represent agents’ knowledge in reasoning. The authors demonstrate how this approach handles the situation where the security agent’s knowledge on access decision is incomplete. The proposed mechanism effectively prevents unauthorized and malicious access to information systems.

Updating Epistemic Logic Programs

We consider the problem of updating non-monotonic knowledge bases represented by epistemic logic programs where disjunctive information and notions of knowledge and belief can be explicitly expressed. We propose a formulation for epistemic logic program update based on a principle called minimal change and maximal coherence. The central feature of our approach is that during an update or a sequence of updates, contradictory information is removed on a basis of minimal change under the semantics of epistemic logic programs and then coherent information is maximally retained in the update result. Through various update scenarios, we show that our approach provides both semantic and syntactic characterizations for an update problem. We also investigate essential semantic properties of epistemic logic program update.

Knowledge and the action description language A

We introduce Ak, an extension of the action description language A (Gelfond and Lifschitz, 1993) to handle actions which affect knowledge. We use sensing actions to increase an agent's knowledge of the world and non-deterministic actions to remove knowledge. We include complex plans involving conditionals and loops in our query language for hypothetical reasoning. We also present a translation of Ak domain descriptions into epistemic logic programs.