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Gossip protocols deal with a group of communicating agents, each holding a private information, and aim at arriving at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols are particularly simple distributed programs that use formulas from an epistemic logic. Recently, the implementability of these distributed protocols was established (which means that the evaluation of these formulas is decidable), and the problems of their partial correctness and termination were shown to be decidable, but their exact computational complexity was left open. We show that for any monotonic type of calls the implementability of a distributed epistemic gossip protocol is a P^{NP}_{||}-complete problem, while the problems of its partial correctness and termination are in coNP^{NP}.
In this article, we provide the epistemic-entrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemic-entrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh’s axiom (P).
We consider the problem of deleting nodes in a covert network to minimize its performance. The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In the MinIGL problem the input is a graph $G$, a budget $k$, and a target IGL $T$, and the question is whether there exists a subset of vertices $X$ with $|X|=k$, such that the IGL of $G-X$ is at most $T$. In network analysis, the IGL is often used to evaluate how well heuristics perform in strengthening or weakening a network. In this paper, we undertake a study of the classical and parameterized complexity of the MinIGL problem. The problem is NP-complete even if $T=0$ and remains both NP-complete and $W[1]$-hard for parameter $k$ on bipartite and on split graphs. On the positive side, we design several multivariate algorithms for the problem. Our main result is an algorithm for MinIGL parameterized by the twin cover number.
We investigate ontology-based query answering (OBQA) in a setting where both the ontology and the query can refer to concrete values such as numbers and strings. In contrast to previous work on this topic, the built-in predicates used to compare values are not restricted to being unary. We introduce restrictions on these predicates and on the ontology language that allow us to reduce OBQA to query answering in databases using the so-called combined rewriting approach. Though at first sight our restrictions are different from the ones used in previous work, we show that our results strictly subsume some of the existing first-order rewritability results for unary predicates.
Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.
We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this notion of equivalence nicely captures the concept of local simplifications. We provide exact characterizations and complexity results for deciding our new notion of equivalence.
Research in abstract argumentation typically per-tains to finite argumentation frameworks (AFs). Ac-tual or potential infinite AFs frequently occur if theyare used for the purpose of nonmonotonic entail-ment, so-called instantiation-based argumentation,or if they are involved as modeling tool for dia-logues, n-person-games or action sequences. Apartfrom these practical cases a profound analysis yieldsa better understanding of how the nonmonotonic the-ory of abstract argumentation works in general. Inthis paper we study a bunch of abstract propertieslike SCC-recursiveness, expressiveness or intertrans-latability for unrestricted AFs.
We address the problem of multicriteria ordinalsorting through the lens of accountability, i.e. theability of a human decision-maker to own a recommendationmade by the system. We put forward anumber of model features that would favor the capabilityto support the recommendation with a convincingexplanation. To account for that, we designa recommender system implementing and formalizingsuch features. This system outputs explanationsdefined under the form of specific argumentschemes tailored to represent the specific rules ofthe model. At the end, we discuss possible andpromising argumentative perspectives.
We introduce a first-order extension of dynamic logic (FO-DL), suitable to represent and reason about the behaviour of Data-aware Systems (DaS), which are systems whose data content is explicitly exhibited in the system’s description. We illustrate the expressivity of the formal framework by modelling English auctions as DaS, and by specifying relevant properties in FO-DL. Most importantly, we develop an abstraction-based verification procedure, thus proving that the model checking problem for DaS against FO-DL is actually decidable, provided some mild assumptions on the interpretationdomain.
When it comes to robotic agents operating in an uncertain world, a major concern in knowledge representation is to better relate high-level logical accounts of belief and action to the low-level probabilistic sensorimotor data. Perhaps the most general formalism for dealing with degrees of belief and, in particular, how such beliefs should evolve in the presence of noisy sensing and acting is the account by Bacchus, Halpern, and Levesque. In this paper, we reconsider that model of belief, and propose a new logical variant that has much of the expressive power of the original, but goes beyond it in novel ways. In particular, by moving to a semantical account of a modal variant of the situation calculus based on possible worlds with unbounded domains and probabilistic distributions over them, we are able to capture the beliefs of a fully introspective knowledge base with uncertainty by way of an only-believing operator. The paper introduces the new logic and discusses key properties as well as examples that demonstrate how the beliefs of a knowledge base change as a result of noisy actions.
We consider a setting where a user wants to pose a query against a dataset where background knowledge, expressed as logical sentences, is available, but only a subset of the information can be used to answer the query. We thus want to reformulate the user query against the subvocabulary, arriving at a query equivalent to the user’s query assuming the background theory, but using only the restricted vocabulary. We consider two variations of the problem, one where we want any such reformulation and another where we restrict the size. We present a classification of the complexity of the problem, then provide algorithms for solving the problems in practice and evaluate their performance.
We propose a novel rule-based ontology language for JSON records and investigate its computational properties. After providing a natural translation into first-order logic, we identify relationships to existing ontology languages, which yield decidability of query answering but only rough complexity bounds. By establishing an interesting and non-trivial connection to word rewriting, we are able to pinpoint the exact combined complexity of query answering in our framework and obtain tractability results for data complexity. The upper bounds are proven using a query reformulation technique, which can be implemented on top of key-value stores, thereby exploiting their querying facilities.
In this paper, we aim to study how the performance of modern answer set programming (ASP) solvers is influenced by the treewidth of the input program and to investigate the consequences of this relationship. We first perform an experimental evaluation that shows that the solving performance is heavily influenced by the treewidth, given ground input programs that are otherwise uniform, both in size and construction. This observation leads to an important question for ASP, namely, how to design encodings such that the treewidth of the resulting ground program remains small. To this end, we define the class of connection-guarded programs, which guarantees that the treewidth of the program after grounding only depends on the treewidth (and the degree) of the input instance. In order to obtain this result, we formalize the grounding process using MSO transductions.
In many knowledge representation formalisms, a constructive semantics is defined based on sequential applications of rules or of a semantic operator. These constructions often share the property that rule applications must be delayed until it is safe to do so: until it is known that the condition that triggers the rule will remain to hold. This intuition occurs for instance in the well-founded semantics of logic programs and in autoepistemic logic. In this paper, we formally define the safety criterion algebraically. We study properties of so-called safe inductions and apply our theory to logic programming and autoepistemic logic. For the latter, we show that safe inductions manage to capture the intended meaning of a class of theories on which all classical constructive semantics fail.
Active integrity constraints (AICs) constitute a formalism to associate with a database not just the constraints it should adhere to, but also how to fix the database in case one or more of these constraints are violated. The intuitions regarding which repairs are “good” given such a description are closely related to intuitions that live in various areas of non-monotonic reasoning. In this paper, we apply approximation fixpoint theory, an algebraic framework that unifies semantics of non-monotonic logics, to the field of AICs. This results in a new family of semantics for AICs, of which we study semantics and relationships to existing semantics. We argue that the AFT-well-founded semantics has some desirable properties.
We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies mu that solve the abstract problem P have been shown to solve all problems Q that reduce to P provided that mu terminates in Q. In this work, we shed light on why this termination condition is needed and how it can be removed. The key observation is that the abstract problem P captures the common structure among the concrete problems Q that is local (Markovian) but misses common structure that is global. We show how such global structure can be captured by means of trajectory constraints that in many cases can be expressed as LTL formulas, thus reducing generalized planning to LTL synthesis. Moreover, for a broad class of problems that involve integer variables that can be increased or decreased, trajectory constraints can be compiled away, reducing generalized planning to fully observable non-deterministic planning.
Cross products form a useful modelling tool that allows us to express natural statements such as "elephants are bigger than mice", or, more generally, to define relations that connect every instance in a relation with every instance in another relation. Despite their usefulness, cross products cannot be expressed using existing guarded ontology languages, such as description logics (DLs) and guarded existential rules. The question that comes up is whether cross products are compatible with guarded ontology languages, and, if not, whether there is a way of making them compatible. This has been already studied for DLs, while for guarded existential rules remains unanswered. Our goal is to give an answer to the above question. To this end, we focus on the guarded fragment of first-order logic (which serves as a unifying framework that subsumes many of the aforementioned ontology languages) extended with cross products, and we investigate the standard tasks of satisfiability and query answering. Interestingly, we isolate relevant fragments that are compatible with cross products.
Shortlisting of candidates—selecting a group of “best” candidates—is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the most natural and simple voting rule in this scenario, l-Bloc (every voter approves l candidates). In particular, we investigate the influence of several tie-breaking mechanisms (e.g. pessimistic versus optimistic) and group evaluation functions (e.g. egalitarian versus utilitarian) and conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. We provide a fairly comprehensive picture of the computational complexity landscape of this neglected scenario.
We consider opinion diffusion in binary influence networks, where at each step one or more agents update their opinions so as to be in agreement with the majority of their neighbors. We consider several ways of manipulating the majority opinion in a stable outcome, such as bribing agents, adding/deleting links, and changing the order of updates, and investigate the computational complexity of the associated problems, identifying tractable and intractable cases.
Minimal inconsistent subsets of knowledge bases play an important role in classical logics, most notably for repair and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play the same role as minimal inconsistent subsets in classical reasoning. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on repair and inconsistency measurement.
We analyze a classical generalized probabilistic satisfiability problem (GGenPSAT) which consists in deciding the satisfiability of Boolean combinations of linear inequalities involving probabilities of classical propositional formulas. GGenPSAT coincides precisely with the satisfiability problem of the probabilistic logic of Fagin et al. and was proved to be NP-complete. Here, we present a polynomial reduction of GGenPSAT to SMT over the quantifier-free theory of linear integer and real arithmetic. Capitalizing on this translation, we implement and test a solver for the GGenPSAT problem. As previously observed for many other NP-complete problems, we are able to detect a phase transition behavior for GGenPSAT.
The paper introduces a notion of a budget-constrained multiagent transition system that associates two financial parameters with each transition: a pre-transition minimal budget requirement and a post-transition profit. The paper also proposes a new modal language for reasoning about such a system. The language uses a modality labeled by agent as well as by budget and profit constraints. The main technical result is a sound and complete logical system that describes all universal properties of this modality. Among these properties is a form of Transitivity axiom that captures the interplay between the budget and profit constraints.
The restricted chase is a sound and complete algorithm for conjunctive query answering over ontologies of disjunctive existential rules. We develop acyclicity conditions to ensure its termination. Our criteria cannot always detect termination (the problem is undecidable), and we develop the first cyclicity criteria to show non-termination of the restricted chase. Experiments on real-world ontologies show that our acyclicity notions improve significantly over known criteria.
Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that it also makes sense to analyse belief change within a (preferential) non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. We show that the results obtained can also be applied to the preservation of coherence— an important notion within the field of logic-based ontologies. We adopt the AGM approach to belief change and show that standard AGM can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results.
We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorithm creates a coarse imperfect recall abstraction of the perfect recall game and automatically refines its information set structure only where the imperfect recall might cause problems. Experimental evaluation shows that our novel algorithm is able to solve a simplified poker game with 7.10^5 information sets using an abstracted game with only 1.8% of information sets of the original game. Additional experiments on poker and randomly generated games suggest that the relative size of the abstraction decreases as the size of the solved games increases.