Mario Alviano

• Ph.D. in Computer Science
• Professor (Associate) at University of Calabria

ASP Chef is a versatile tool built upon the principles of Answer Set Programming (ASP), offering a unique approach to problem-solving through the concept of ASP recipes. In this paper, we explore two key components of ASP Chef: the Graph ingredient and one of its extension mechanisms for registering new ingredients. The Graph ingredient serves as a...

In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties. We also consider an i...

Weighted knowledge bases for description logics with typicality under a ‘concept-wise’ multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a $\varPi ^{p}_{2}...

Aggregates such as sum and count are among the most frequently used linguistic extensions of Answer Set Programming (ASP). At-most-one (AMO) constraints are a specific form of aggregates that excludes the simultaneous truth of multiple elements in a set. This article unleashes a powerful propagation strategy in case groups of elements in an aggrega...

Explainable artificial intelligence (XAI) aims at addressing complex problems by coupling solutions with reasons that justify the provided answer. In the context of Answer Set Programming (ASP) the user may be interested in linking the presence or absence of an atom in an answer set to the logic rules involved in the inference of the atom. Such exp...

Weighted knowledge bases for description logics with typicality provide a logical interpretation of MultiLayer Perceptrons, based on a “concept-wise” multi-preferential semantics. On the one hand, in the finitely many-valued case, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning from weighted knowledge...

Marketplaces bring together products from multiple providers and automatically manage orders that involve several suppliers. We document the use of Answer Set Programming to automatically choose products from various warehouses within a marketplace network to fulfill a specified order. The proposed solution seamlessly adapts to various objective fu...

Generative Datalog is an extension of Datalog that incorporates constructs for referencing parameterized probability distributions. This augmentation transforms the evaluation of a Generative Datalog program into a stochastic process, resulting in a declarative formalism suitable for modeling and analyzing other stochastic processes. This work prov...

Weighted knowledge bases for description logics with typicality under a “concept-wise” multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a \(\varPi ^p_2\)...

In imperative programming, the Domain-Driven Design methodology helps in coping with the complexity of software development by materializing in code the invariants of a domain of interest. Code is cleaner and more secure because any implicit assumption is removed in favor of invariants, thus enabling a fail fast mindset and the immediate reporting...

In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with typicality are considered under a (many-valued) ``concept-wise" multipreference semantics. The semantics is used...

Weighted knowledge bases for description logics with typicality under a "concept-wise'' multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a $\Pi^p_2$ upper...

Marketplaces aggregate products from several providers and handle orders involving several suppliers automatically. We report on an application of Answer Set Programming for automatically selecting products from different warehouses within the network of a marketplace to fulfill a given order. The presented solution easily accommodates different ob...

In imperative programming, the Domain-Driven Design methodology helps in coping with the complexity of software development by materializing in code the invariants of a domain of interest. Code is cleaner and more secure because any implicit assumption is removed in favor of invariants, thus enabling a fail fast mindset and the immediate reporting...

Several AI problems can be conveniently modelled in ASP, and many of them require to enumerate solutions characterized by an optimality property that can be expressed in terms of subset-minimality with respect to some objective atoms. In this context, solutions are often either (i) answer sets or (ii) sets of atoms that enforce the absence of answe...

Modal logic S5 is used extensively for representing knowledge that includes statements about necessity and possibility, owing to its simplicity in handling chained modal operators. Significant research effort has been devoted in developing efficient reasoning mechanisms over complex S5 formulas, resulting in various solvers taking advantage of the...

The development of complex software requires tools promoting fail-fast approaches, so that bugs and unexpected behavior can be quickly identified and fixed. Tools for data validation may save the day of computer programmers. In fact, processing invalid data is a waste of resources at best, and a drama at worst if the problem remains unnoticed and w...

Answer set programming (ASP) emerged in the late 1990s as a paradigm for knowledge representation and reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has b...

Answer Set Programming (ASP) emerged in the late 1990ies as a paradigm for Knowledge Representation and Reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has...

The pyglaf reasoner takes advantage of circumscription to solve computational problems of abstract argumentation frameworks. In fact, many of these problems are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Within pyglaf, Python is used to build...

Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducin...

Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducin...

Data validation may save the day of computer programmers, whatever programming language they use. In fact, processing invalid data is a waste of resources at best, and a drama at worst if the problem remains unnoticed and wrong results are used for business. Answer Set Programming is not an exception, but the quest for better and better performance...

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and l...

Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of Datalog queries. This paper surveys some of these compilations, and in particular the one addressing queries ove...

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, wa...

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, wa...

The paper presents DLV, an advanced AI system from the area of Answer Set Programming (ASP), showing its high potential for reasoning over ontologies. Ontological reasoning services represent fundamental features in the development of the Semantic Web. Among them, scientists are focusing their attention on the so-called ontology-based query answeri...

Answer Set Programming (ASP) is a well-known declarative problem solving paradigm developed in the field of nonmonotonic reasoning and logic programming. The usual target of ASP is the solution of combinatorial search problems, nonetheless the language of ASP was extended with weak constraints for concise modelling of optimization problems. In the...

Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of Datalog queries. This paper surveys some of these compilations, and in particular the one addressing queries ove...

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down...

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far fr...

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far fr...

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down...

Answer Set Programming (ASP) has seen several extensions by generalizing the notion of atom used in these programs, for example dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints, referred to collectively as generalized atoms in this paper. The idea common to all of these constructs is that their satisfaction de...

This book constitutes the proceedings of the XVIIIth International Conference of the Italian Association for Artificial Intelligence, AI*IA 2019, held in Rende, Italy, in November 2019. The 41 full papers were carefully reviewed and selected from 67 submissions. The papers have been organized in the following topical sections: Knowledge Representa...

Coalition formation is studied in a setting where agents take part to a group decision-making scenario and where their preferences are expressed via weighted propositional logic, in particular by considering formulas consisting of conjunctions of literals only. Interactions among agents are constrained by an underlying social environment and each a...

Answer set programming (ASP) is a declarative language for nonmonotonic reasoning based on stable model semantics.Astable model is a classical model of the input program satisfying the following stability condition: only necessary information is included in the model under the assumptions provided by the model itself for the unknown knowledge in th...

Propositional circumscription defines a preference relation over the models of a propositional theory, so that models being subset-minimal on the interpretation of a set of objective atoms are preferred.The complexity of several computational tasks increase by one level in the polynomial hierarchy due to such a preference relation;among them there...

Aggregates are among the most important linguistic extensions of Answer Set Programming (ASP), allowing for compact representations of properties and inductive definitions involving sets of propositions. Common use cases of aggregates in ASP are reported in this paper, which mainly focus on the semantics implemented by mainstream solvers, namely th...

We briefly describe the answer set programming system DLV, focusing on some of its peculiar features and mentioning a number of successful applications.

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an...

Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When the aggregation involves literals whose truth value is undefined at instantiation time, modern grounders intro...

Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When the aggregation involves literals whose truth value is undefined at instantiation time, modern grounders intro...

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an...

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their...

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their...

The goal of the Nurse Scheduling Problem (NSP) is to find an assignment of nurses to shifts according to specific requirements. Given its practical relevance, many researchers have developed different strategies for solving several variants of the problem. One of such variants was recently addressed by an approach based on Answer Set Programming (A...

Efficient algorithms for the computation of optimum stable models are based on unsatisfiable core analysis. However, these algorithms essentially run to completion, providing few or even no suboptimal stable models. This drawback can be circumvented by shrinking unsatisfiable cores. Interestingly, the resulting anytime algorithm can solve more inst...

Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is sufficient to cause the observed anomaly. Alternatively, a minimal correction subset comprises a minimal set of reaso...

We introduce Open image in new window, a new Answer Set Programming (ASP) system. Open image in new window combines Open image in new window, a fully-compliant ASP-Core-2 grounder, with the well-assessed solver Open image in new window. Input programs may be enriched by annotations and directives that customize heuristics of the system and extend i...

Normal tuple-generating dependencies (NTGDs) are TGDs enriched with default negation, a.k.a. negation as failure. Query answering under NTGDs, where negation is interpreted according to the stable model semantics, is an intriguing new problem that gave rise to flourishing research activity in the database and KR communities. So far, all the existin...

Fuzzy Answer Set Programming (FASP) combines the non-monotonic reasoning typical of Answer Set Programming with the capability of Fuzzy Logic to deal with imprecise information and paraconsistent reasoning. In the context of paraconsistent reasoning, the fundamental principle of minimal undefinedness states that truth degrees close to 0 and 1 shoul...

Aggregation functions are widely used in answer set programming (ASP) for representing and reasoning on knowledge involving sets of objects collectively. These sets may also depend recursively on the results of the aggregation functions, even if so far the support for such recursive aggregations was quite limited in ASP systems. In fact, recursion...

Modern, efficient Answer Set Programming solvers implement answer set search via non-chronological backtracking algorithms. The extension of these algorithms to answer set enumeration is nontrivial. In fact, adding blocking constraints to discard already computed answer sets is inadequate because the introduced constraints may not fit in memory or...

Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented her...

Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented her...

Boolean functions in Answer Set Programming have proven a useful modelling tool. They are usually specified by means of aggregates or external atoms. A crucial step in computing answer sets for logic programs containing Boolean functions is verifying whether partial interpretations satisfy a Boolean function for all possible values of its undefined...

ASP solvers address several reasoning tasks that go beyond the mere computation of answer sets. Among them are cautious reasoning, for modeling query entailment, and optimum answer set computation, for supporting numerical optimization. This paper reports on the recent improvements of the solver wasp, and details the algorithms and the design choic...

Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are dl-atoms, aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper w...

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the \Godel and \Luka fuzzy connectives are usually considered, due to their properties....

Gelfond and Zhang recently proposed a new stable model semantics based on Vicious Circle Principle in order to improve the interpretation of logic programs with aggregates. The paper focuses on this proposal, and analyzes the complexity of both coherence testing and cautious reasoning under the new semantics. Some surprising results highlight simil...

Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since th...

The problem of query answering under the well-founded and stable model semantics for normal existential rules, that is, existential rules enriched with default negation, has recently attracted a lot of interest from the database and KR communities. In particular, it has been thoroughly studied for classes of normal existential rules that are based...

NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to answer set programming (ASP), so far the only existing implementations are by means of Prolog and via Boolean satisfiability solvers. In this pap...

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequ...

Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to...

Answer Set Programming (ASP) is a declarative programming paradigm. The intrinsic complexity of the evaluation of ASP programs makes the development of more effective and faster systems a challenging research topic. This paper reports on the recent improvements of the ASP solver WASP. WASP is undergoing a refactoring process which will end up in th...

Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and antimonotone aggregates (LPAma programs). In particular, we present a new notion of unfounded set for LPAma pro...

In recent years, Answer Set Programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms, generalized quantifiers, or abstract constraints, the idea is to have more complicated satisfaction patterns in the la...

Answer Set Programming (ASP) is a logic programming language for nonmonotonic reasoning. Propositional ASP programs are usually evaluated by DPLL algorithms combining unit propagation with operators that are specific of ASP. Among them, unfounded set propagation is used for handling recursive programs by many ASP solvers. This paper reports a compa...

This paper introduces WASP, an ASP solver handling disjunctive logic programs under the stable model semantics. WASP implements techniques originally introduced for SAT solving that have been extended to cope with ASP programs. Among them are restarts, conflict-driven constraint learning and backjumping. Moreover, WASP combines these SAT-based tech...

In recent years, answer set programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms, generalized quantifiers, or abstract constraints, the idea is to have more complicated satisfaction patterns in the la...

Answer Set Programming is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, PDDL and many others. Since its first informal editions, ASP systems are compared in the nowadays customary ASP Competition. The fourth ASP Competition, held...

Fuzzy answer set programming (FASP) is a recent formalism for knowledge representation that enriches the declarativity of answer set programming by allowing propositions to be graded. To now, no implementations of FASP solvers are available and all current proposals are based on compilations of logic programs into different paradigms, like mixed in...

NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present tr...

The paper discusses the impact of adding existential quantification in the head of positive disjunctive Datalog rules. After introducing syntax and semantics of the resulting language, we provide a notion of instantiation, which has been proven to be adequate for query answering purposes. Although on the one hand this new formalism is attractive fo...

Adapting techniques from database theory in order to optimize Answer Set Programming (ASP) systems, and in particular the grounding components of ASP systems, is an important topic in ASP. In recent years, the Magic Set method has received some interest in this setting, and a variant of it, called Dynamic Magic Set, has been proposed for ASP. Howev...

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integra...

Datalog ∃ is the extension of Datalog allowing existentially quantified variables in rule heads. This language is highly expressive and enables easy and powerful knowledge-modelling, but the presence of existentially quantified variables makes reasoning over Datalog ∃ undecidable in the general case. Restricted classes of Datalog ∃ , such as shy, h...

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimization technique. An important feature of disjunctive Datalog is nonmonotonicity, which calls for nond...

The explosive growth and popularity of the Web has resulted in a huge amount of digital information sources on the Internet. Unfortunately, such sources only manage data, rather than the knowledge they carry. Recognizing, extracting, and structuring relevant information according to their semantics is a crucial task. Several approaches in the field...

Answer Set Programming is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, FO(.), PDDL and many others. Since its first informal editions, ASP systems are compared in the nowadays customary ASP Competition. The Third ASP Competition...

Disjunctive Logic Programming (DLP) is an extension of Datalog that allows for disjunction in rule head and nonmonotonic negation in bodies. All of the queries in the second level of the polynomial hierarchy can be expressed in this language. However, DLP does not allow for representing properties which involve sets of data in a natural way. Extend...