A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By “traditional” classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper, we fill the gaps remaining in an

The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical

In this note, we use Kunen’s notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate p that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of p. The second theorem

We present a general logical framework for reasoning about agents’ cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire, and preference. We also present two extensions

Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few components, and it is desirable to reuse as much as possible previous analysis results. This has been achieved to date through incremental global analysis fixpoint algorithms

This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and new directives allowing the proximity equations linking two words to be generated with an approximation degree. Proximity equations are the key syntactic structures

Bounded treewidth is one of the most cited combinatorial invariants in the literature. It was also applied for solving several counting problems efficiently. A canonical counting problem is #Sat, which asks to count the satisfying assignments of a Boolean formula. Recent work shows that benchmarking instances for #Sat often have reasonably small treewidth. This paper deals with counting problems for

Deploying Internet of Things (IoT)-enabled virtual network function (VNF) chains to Cloud-Edge infrastructures requires determining a placement for each VNF that satisfies all set deployment requirements as well as a software-defined routing of traffic flows between consecutive functions that meets all set communication requirements. In this article, we present a declarative solution, EdgeUsher, to

We extend probabilistic action language $p{\cal BC}$+ with the notion of utility in decision theory. The semantics of the extended $p{\cal BC}$+ can be defined as a shorthand notation for a decision-theoretic extension of the probabilistic answer set programming language LPMLN. Alternatively, the semantics of $p{\cal BC}$+ can also be defined in terms of Markov decision process (MDP), which in turn

The manipulation of articulated objects is of primary importance in Robotics and can be considered as one of the most complex manipulation tasks. Traditionally, this problem has been tackled by developing ad hoc approaches, which lack flexibility and portability. In this paper, we present a framework based on answer set programming (ASP) for the automated manipulation of articulated objects in a robot

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts

ISO Prolog provides catch and throw to realize the control flow of exception handling. This pearl demonstrates that catch and throw are inconspicuously amenable to the implementation of backjumping. In fact, they have precisely the semantics required: rewinding the search to a specific point and carrying of a preserved term to that point. The utility of these properties is demonstrated through an implementation

For some applications, standard resource analyses do not provide the information required. Such analyses estimate the total resource usage of a program (without executing it) as functions on input data sizes. However, some applications require knowing how such total resource usage is distributed over selected parts of a program. We propose a novel, general, and flexible framework for setting up cost

On top of a neural network-based dependency parser and a graph-based natural language processing module, we design a Prolog-based dialog engine that explores interactively a ranked fact database extracted from a text document. We reorganize dependency graphs to focus on the most relevant content elements of a sentence and integrate sentence identifiers as graph nodes. Additionally, after ranking the

Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations, necessary in some cases to get the correct meaning. We provide a detailed formal account of an extension of logic programming supporting flexible coinduction. Syntactically

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

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes

Decision support systems play an important role in medical fields as they can augment clinicians to deal more efficiently and effectively with complex decision-making processes. In the diagnosis of headache disorders, however, existing approaches and tools are still not optimal. On the one hand, to support the diagnosis of this complex and vast spectrum of disorders, the International Headache Society

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model. In this paper, we continue the study of justification theory by means of three major contributions

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP( $\mathcal A \mathcal C$ )), where rules may contain constraints that

The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are

The paper describes an ongoing effort in developing a declarative system for supporting operators in the Nuclear Power Plant (NPP) control room. The focus is on two modules: diagnosis and explanation of events that happened in NPPs. We describe an Answer Set Programming (ASP) representation of an NPP, which consists of declarations of state variables, components, their connections, and rules encoding

We propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic

The W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks, expressive yet decidable fragments have been identified. Among them, we focus on OWL 2 RL, which offers a rich variety of semantic constructors, apart from supporting all

The multi-agent path finding (MAPF) problem is a combinatorial search problem that aims at finding paths for multiple agents (e.g., robots) in an environment (e.g., an autonomous warehouse) such that no two agents collide with each other, and subject to some constraints on the lengths of paths. We consider a general version of MAPF, called mMAPF, that involves multi-modal transportation modes (e.g

In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen’s classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension

For planning an assembly of a product from a given set of parts, robots necessitate certain cognitive skills: high-level planning is needed to decide the order of actuation actions, while geometric reasoning is needed to check the feasibility of these actions. For collaborative assembly tasks with humans, robots require further cognitive capabilities, such as commonsense reasoning, sensing, and communication

Designing agents that reason and act upon the world has always been one of the main objectives of the Artificial Intelligence community. While for planning in “simple” domains the agents can solely rely on facts about the world, in several contexts, e.g., economy, security, justice and politics, the mere knowledge of the world could be insufficient to reach a desired goal. In these scenarios, epistemic

Answer-Set Programming (ASP) is a powerful and expressive knowledge representation paradigm with a significant number of applications in logic-based AI. The traditional ground-and-solve approach, however, requires ASP programs to be grounded upfront and thus suffers from the so-called grounding bottleneck (i.e., ASP programs easily exhaust all available memory and thus become unsolvable). As a remedy

Efficient decision-making over continuously changing data is essential for many application domains such as cyber-physical systems, industry digitalization, etc. Modern stream reasoning frameworks allow one to model and solve various real-world problems using incremental and continuous evaluation of programs as new data arrives in the stream. Applied techniques use, e.g., Datalog-like materialization

In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable

We focus on the problem of inducing logic programs that explain models learned by the support vector machine (SVM) algorithm. The top-down sequential covering inductive logic programming (ILP) algorithms (e.g., FOIL) apply hill-climbing search using heuristics from information theory. A major issue with this class of algorithms is getting stuck in local optima. In our new approach, however, the data-dependent

Concolic testing is a popular software verification technique based on a combination of concrete and symbolic execution. Its main focus is finding bugs and generating test cases with the aim of maximizing code coverage. A previous approach to concolic testing in logic programming was not sound because it only dealt with positive constraints (by means of substitutions) but could not represent negative

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation

Recently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF

The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground programs thus achieving a significant payoff in terms of computing time. However, this may require some additional amount of memory and/or the manual addition of operational

This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware

In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the problem encoded by P, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved

We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its

Generalising and re-using knowledge learned while solving one problem instance has been neglected by state-of-the-art answer set solvers. We suggest a new approach that generalises learned nogoods for re-use to speed-up the solving of future problem instances. Our solution combines well-known ASP solving techniques with deductive logic-based machine learning. Solving performance can be improved by

Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original

The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance

Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases

Answer set programming (ASP) is a paradigm for modeling knowledge-intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting

Epistemic logic programs constitute an extension of the stable model semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some objective literal is true in all or some stable models. As it can be imagined, the associated semantics has proved to be non-trivial, since the truth of subjective literals may interfere with the

We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to account for a fine-grained timing. More precisely, we exemplarily show how the hybrid ASP system clingo[DL] can be used to tackle demanding planning and scheduling

In order to automatically infer the resource consumption of programs, analyzers track how data sizes change along program’s execution. Typically, analyzers measure the sizes of data by applying norms which are mappings from data to natural numbers that represent the sizes of the corresponding data. When norms are defined by taking type information into account, they are named typed-norms. This article

This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully

Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third

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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

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data,

We present OntoScene, a framework aimed at understanding the semantics of visual scenes starting from the semantics of their elements and the spatial relations holding between them. OntoScene exploits ontologies for representing knowledge and Prolog for specifying the interpretation rules that domain experts may adopt, and for implementing the SceneInterpreter engine. Ontologies allow the designer