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Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Preferences in AF allow to represent the comparative strength of arguments in a simple yet expressive way. Preference-based AF (PAF) has been proposed to extend AF with preferences of the form a > b, whose intuitive meaning is that argument a is better than b. In this paper we generalize PAF by introducing conditional preferences of the form a > b \leftarrow body that informally state that a is better than b whenever the condition expressed by body is true. The resulting framework, namely Conditional Preference-based AF (CPAF), extends the PAF semantics under three well-known preference criteria, i.e. democratic, elitist, and KTV. After introducing CPAF, we study the complexity of the verification problem (deciding whether a set of arguments is a ``best'' extension) as well as of the credulous and skeptical acceptance problems (deciding whether a given argument belongs to any or all ``best'' extensions, respectively) under multiple-status semantics (that is, complete, preferred, stable, and semi-stable semantics) for the above-mentioned preference criteria.
We study the synthesis under environment specifications problem for LTL/LTLf which, in particular, generalizes FOND (strong) planning with these temporal goals. We consider the case where the agent cannot enforce its goal --- for which the argument for using best-effort strategies has been made --- and study the intermediate ground, between enforcing and best-effort strategies, of dominant strategies. Intuitively, such strategies achieve the goal against any environment for which it is achievable. We show that dominant strategies may exist when enforcing ones do not, while still sharing with the latter many desirable properties such as being interchangeable with each other, and being monotone with respect to tightening of environment specifications. We give necessary and sufficient conditions for the existence of dominant strategies, and show that deciding if they exist is 2EXPTIME-complete --- the same as for enforcing strategies. Finally, we give a uniform, optimal, game-theoretic algorithm for simultaneously solving the three synthesis problems of enforcing, dominant, and best-effort strategies.
Linear Temporal Logic (LTL) is the de-facto standard temporal logic for system specification, whose foundational properties have been studied for over five decades. Safety and cosafety properties of LTL define notable fragments of LTL, where a prefix of a trace suffices to establish whether a formula is true or not over that trace. In this paper, we study the complexity of the problems of satisfiability, validity, and realizability over infinite and finite traces for the safety and cosafety fragments of LTL. As for satisfiability and validity over infinite traces, we prove that the majority of the fragments have the same complexity as full LTL, that is, they are PSPACE-complete. The picture is radically different for realizability: we find fragments with the same expressive power whose complexity varies from 2EXPTIME-complete (as full LTL) to EXPTIME-complete. Notably, for all cosafety fragments, the complexity of the three problems does not change passing from infinite to finite traces, while for all safety fragments the complexity of satisfiability (resp., realizability) over finite traces drops to NP-complete (resp., Πᴾ₂- complete).
We propose a new approach to the verification of epistemic properties of programmes. First, we introduce the new ``program-epistemic'' logic L_PK, which is strictly richer and more general than similar formalisms appearing in the literature. To solve the verification problem in an efficient way, we introduce a translation from our language L_PK into first-order logic. Then, we show and prove correct a reduction from the model checking problem for program-epistemic formulas to the satisfiability of their first-order translation. Both our logic and our translation can handle richer specification w.r.t. the state of the art, allowing us to express the knowledge of agents about facts pertaining to programs (i.e., agents' knowledge before a program is executed as well as after is has been executed). Furthermore, we implement our translation in Haskell in a general way (i.e., independently of the programs in the logical statements), and we use existing SMT-solvers to check satisfaction of L_PK formulas on a benchmark example in the AI/agency field.
In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to different classes of claim-augmented argumentation frameworks, and behave differently in terms of semantic properties and computational complexity. This strengthens the view that the actual choice for handling preferences has to be taken with care.
Microaggregation is a classical statistical disclosure control technique which requires the input data to be partitioned into clusters while adhering to specified size constraints. We provide novel exact algorithms and lower bounds for the task of microaggregating a given network while considering both unrestricted and connected clusterings, and analyze these from the perspective of the parameterized complexity paradigm. Altogether, our results assemble a complete complexity-theoretic picture for the network microaggregation problem with respect to the most natural parameterizations of the problem, including input-specified parameters capturing the size and homogeneity of the clusters as well as the treewidth and vertex cover number of the network.
In the context of verification of data-aware processes, a formal approach based on satisfiability modulo theories (SMT) has been considered to verify parameterised safety properties. This approach requires a combination of model-theoretic notions and algorithmic techniques based on backward reachability. We introduce here Ontology-Based Processes, which are a variant of one of the most investigated models in this spectrum, namely simple artifact systems (SASs), where, instead of managing a database, we operate over a description logic (DL) ontology. We prove that when the DL is expressed in (a slight extension of) RDFS, it enjoys suitable model-theoretic properties, and that by relying on such DL we can define Ontology-Based Processes to which backward reachability can still be applied. Relying on these results we are able to show that in this novel setting, verification of safety properties is decidable in PSPACE.
The Datalog query language can express several powerful recursive properties, often crucial in real-world scenarios. While answering such queries is feasible over relational databases, the picture changes dramatically when data is enriched with intensional knowledge. It is indeed well-known that answering Datalog queries is undecidable already over lightweight knowledge bases (KBs) of the DL-Lite family. To overcome this issue, we propose a new query language based on Disjunctive Datalog rules combined with a modal epistemic operator. Rules in this language interact with the queried KB exclusively via the epistemic operator, thus extracting only the information true in every model of the KB. This form of interaction is crucial for not falling into undecidability. The contribution provided by this paper is threefold. First, we illustrate the syntax and the semantics of the novel query language. Second, we study the expressive power of different fragments of our new language and compare it with Disjunctive Datalog and its variants. Third, we outline the precise data complexity of answering queries in our new language over KBs expressed in various well-known formalisms.
The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first discovers "where not to search". We use given BK to discover constraints on hypotheses, such as that a number cannot be both even and odd. We use the constraints to bootstrap a constraint-driven ILP system. Our experiments on multiple domains (including program synthesis and inductive general game playing) show that our approach can (i) substantially reduce learning times by up to 97%, and (ii) can scale to domains with millions of facts.
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we introduce a general framework to convert a large class of width-based model-checking algorithms into algorithms that can be used to test the validity of graph-theoretic conjectures on classes of graphs of bounded width. Our framework is modular and can be applied with respect to several well-studied width measures for graphs, including treewidth and cliquewidth. As a quantitative application of our framework, we prove analytically that for several long-standing graph-theoretic conjectures, there exists an algorithm that takes a number k as input and correctly determines in time double-exponential in a polynomial of k whether the conjecture is valid on all graphs of treewidth at most k. These upper bounds, which may be regarded as upper-bounds on the size of proofs/disproofs for these conjectures on the class of graphs of treewidth at most k, improve significantly on theoretical upper bounds obtained using previously available techniques.
We investigate the complexity of the model-checking problem for a family of modal logics capturing the notion of “knowing how”. We consider the most standard ability-based knowing how logic, for which we show that model-checking is PSpace-complete. By contrast, a multi-agent variant based on an uncertainty relation between plans in which uncertainty is encoded by a regular language, is shown to admit a PTime model-checking problem. We extend with budgets the above-mentioned ability-logics, as done for ATL-like logics. We show that for the former logic enriched with budgets, the complexity increases to at least ExpSpace-hardness, whereas for the latter, the PTime bound is preserved. Other variant logics are discussed along the paper.
Synchronous dynamical systems are well-established models that have been used to capture a range of phenomena in networks, including opinion diffusion, spread of disease and product adoption. We study the three most notable problems in synchronous dynamical systems: whether the system will transition to a target configuration from a starting configuration, whether the system will reach convergence from a starting configuration, and whether the system is guaranteed to converge from every possible starting configuration. While all three problems were known to be intractable in the classical sense, we initiate the study of their exact boundaries of tractability from the perspective of structural parameters of the network by making use of the more fine-grained parameterized complexity paradigm. As our first result, we consider treewidth - as the most prominent and ubiquitous structural parameter - and show that all three problems remain intractable even on instances of constant treewidth. We complement this negative finding with fixed-parameter algorithms for the former two problems parameterized by treedepth, a well-studied restriction of treewidth. While it is possible to rule out a similar algorithm for convergence guarantee under treedepth, we conclude with a fixed-parameter algorithm for this last problem when parameterized by treedepth and the maximum in-degree.
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.
Solving reachability games is a fundamental problem for the analysis, verification, and synthesis of reactive systems. We consider logical reachability games modulo theories (in short, GMTs), i.e., infinite-state games whose rules are defined by logical formulas over a multi-sorted first-order theory. Our games have an asymmetric constraint: the safety player has at most k possible moves from each game configuration, whereas the reachability player has no such limitation. Even though determining the winner of such a GMT is undecidable, it can be reduced to the well-studied problem of checking the satisfiability of a system of constrained Horn clauses (CHCs), for which many off-the-shelf solvers have been developed. Winning strategies for GMTs can also be computed by resorting to suitable CHC queries. We demonstrate that GMTs can model various relevant real-world games, and that our approach can effectively solve several problems from different domains, using Z3 as the backend CHC solver.
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and to prove the correctness of programs. We generalize the conditions under which this technique is applicable, by considering not only dependencies between predicates but also their arguments and context. This allows splitting programs commonly used in practice to which previous results were not applicable.
We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible finite-length, future continuations. This makes monitoring at least as hard as satisfiability and validity. Traces consist of finite sequences of assignments of a fixed set of variables to numerical values. Properties are specified in a logic we call ALTLf, combining LTLf (LTL on finite traces) with linear arithmetic constraints that may carry lookahead, i.e., variables may be compared over multiple instants of the trace. While the monitoring problem for this setting is undecidable in general, we show decidability for (a) properties without lookahead, and (b) properties with lookahead that satisfy the abstract, semantic condition of finite summary, studied before in the context of model checking. We then single out concrete, practically relevant classes of constraints guaranteeing finite summary. Feasibility is witnessed by a prototype implementation.
Dynamical systems are general models of change or movement over time with a broad area of applicability to many branches of science, including computer science and AI. Dynamic topological logic (DTL) is a formal framework for symbolic reasoning about dynamical systems. DTL can express various liveness and reachability conditions on such systems, but has the drawback that the only known axiomatisation requires an extended language. In this paper, we consider dynamic topological logic restricted to the class of scattered spaces. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original language of DTL. In particular, we show that the version of DTL based on the class of scattered spaces is finitely axiomatisable, and that the natural axiomatisation is sound and complete.
Answer Set Programming (ASP) is a prominent modeling and solving framework. An inconsistent core (IC) of an ASP program is an inconsistent subset of rules. In the case of inconsistent programs, a smallest or subset-minimal IC contains crucial rules for the inconsistency. In this work, we study fnding minimal ICs of ASP programs and key fragments from a complexity-theoretic perspective. Interestingly, due to ASP’s non-monotonic behavior, also consistent programs admit ICs. It turns out that there is an entire landscape of problems involving ICs with a diverse range of complexities up to the fourth level of the Polynomial Hierarchy. Deciding the existence of an IC is, already for tight programs, on the second level of the Polynomial Hierarchy. Furthermore, we give encodings for IC-related problems on the fragment of tight programs and illustrate feasibility on small instance sets.
The disjunctive skolem chase is a sound, complete, and potentially non-terminating procedure for solving boolean conjunctive query entailment over knowledge bases of disjunctive existential rules. We develop novel acyclicity and cyclicity notions for this procedure; that is, we develop sufficient conditions to determine chase termination and non-termination. Our empirical evaluation shows that our novel notions are significantly more general than existing criteria.
Taxonomy is formulated as directed acyclic graphs or trees of concepts that support many downstream tasks. Many new coming concepts need to be added to an existing taxonomy. The traditional taxonomy expansion task aims only at finding the best position for new coming concepts in the existing taxonomy. However, they have two drawbacks when being applied to the real-scenarios. The previous methods suffer from low-efficiency since they waste much time when most of the new coming concepts are indeed noisy concepts. They also suffer from low-effectiveness since they collect training samples only from the existing taxonomy, which limits the ability of the model to mine more hypernym-hyponym relationships among real concepts. This paper proposes a pluggable framework called Generative Adversarial Network for Taxonomy Entering Evaluation (GANTEE) to alleviate these drawbacks. A generative adversarial network is designed in this framework by discriminative models to alleviate the first drawback and the generative model to alleviate the second drawback. Two discriminators are used in GANTEE to provide long-term and short-term rewards, respectively. Moreover, to further improve the efficiency, pre-trained language models are used to retrieve the representation of the concepts quickly. The experiments on three real-world large-scale datasets with two different languages show that GANTEE improves the performance of the existing taxonomy expansion methods in both effectiveness and efficiency.
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is crucial when we consider limited agents and reasoning algorithms. Moreover, having the input as arbitrary set of models is more general than the usual treatment of formulas as input. In this setting, we define new Belief Change operations akin to traditional expansion and contraction, and we identify the rationality postulates that emerge due to the finite representability requirement. We also analyse different logics concerning compatibility with our framework.
The ability to understand and generate similes is an imperative step to realize human-level AI. However, there is still a considerable gap between machine intelligence and human cognition in similes, since deep models based on statistical distribution tend to favour high-frequency similes. Hence, a large-scale symbolic knowledge base of similes is required, as it contributes to the modeling of diverse yet unpopular similes while facilitating additional evaluation and reasoning. To bridge the gap, we propose a novel framework for large-scale simile knowledge base construction, as well as two probabilistic metrics which enable an improved understanding of simile phenomena in natural language. Overall, we construct MAPS-KB, a million-scale probabilistic simile knowledge base, covering 4.3 million triplets over 0.4 million terms from 70 GB corpora. We conduct sufficient experiments to justify the effectiveness and necessity of the methods of our framework. We also apply MAPS-KB on three downstream tasks to achieve state-of-the-art performance, further demonstrating the value of MAPS-KB. Resources of MAPS-KB are publicly available at https://github.com/Abbey4799/MAPS-KB.
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 density of a program, the evaluation of the well-known class of normal programs is expected to be slightly harder than deciding satisfiability (SAT). However, it is unclear how to utilize this structural power of ASP. This paper deals with a novel reduction from SAT to normal ASP that goes beyond well-known encodings: We explicitly utilize the structural power of ASP, whereby we sublinearly decrease the treewidth, which probably cannot be significantly improved. Then, compared to existing results, this characterizes hardness in a fine-grained way by establishing the required functional dependency of the dependency graph’s cycle length (SCC size) on the treewidth.
Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.
Learning programs with numerical values is fundamental to many AI applications, including bio-informatics and drug design. However, current program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values from multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NumSynth, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.