The goal of this paper is to benchmark Answer Set Programming (ASP) systems to test their performance when dealing with a complex optimization problem. In particular, the problem tackled is resource allocation in the area of Business Process Management (BPM). Like many other scheduling problems, the allocation of resources and starting times to business process activities is a challenging optimization problem for ASP solvers. Our problem encoding is ASP Core-2 standard compliant and it is realized in a declarative and compact fashion. We develop an instance generator that produces problem instances of different size and hardness with respect to adjustable parameters. By using the baseline encoding and the instance generator, we provide a comparison between the two award-winning ASP solvers clasp and wasp and report the grounding performance of gringo and i-dlv. The benchmark suggests that there is room for improvement concerning both the grounders and the solvers. Fostered by the relevance of the problem addressed, of which several variants have been described in different domains, we believe this is a solid application-oriented benchmark for the ASP community. / Series: Working Papers on Information Systems, Information Business and Operations

It is recognised that normative systems, and in particular electronic institutions and contracts are a potentially powerful means for making agent interactions in multi-agent systems effective and efficient. However, correctly specifying the behaviour of such systems is a difficult problem. Designers are faced with two concurrent, complex tasks: firstly they must specify the relationships (over time) between agents’ actions and their effects, and secondly they must also consider how agents’ actions are to be regulated through the definition of agents’ permissions and obligations. Such systems are typi- cally complex, and given this complexity it may be difficult for a designer to determine whether their original objectives have been captured by the specification of the system. In this dissertation we seek to address some of the problems associated with institu- tional specification. In order to do this we present a model for specifying institutions based on the notion of socially constructed reality that accounts not only for how the action and events which constitute the institution are described, but also how they are regulated. Institutions may be used in a number of ways, and may account for concepts at varying levels of abstraction. Recognising this we also investigate how several insti- tutions, each accounting for a particular aspect of a society may be composed and how the relationships between these institutions may be expressed. Given this model, we then demonstrate how, using the answer set programming paradigm institutional spec- ifications based on our model may be checked for the absence or presence of certain (un)desirable properties.

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Answer set programming (ASP) is a declarative programming paradigm oriented towards difficult combinatorial search problems. Syntactically, ASP programs look like Prolog programs, but solutions are represented in ASP by sets of atoms, and not by substitutions, as in Prolog. Answer set systems, such as Smodels, Smodelscc, and DLV, compute answer sets of a given program in the sense of the answer set (stable model) semantics. This is different from the functionality of Prolog systems, which determine when a given query is true relative to a given logic program. ASP has been applied to many areas of science and technology, from the design of a decision support system for the Space Shuttle to graph-theoretic problems arising in zoology and linguistics. The "native" answer set systems mentioned above are based on specialized search procedures. Usually these procedures are described fairly informally with the use of pseudocode. We propose an alternative approach to describing algorithms of answer set solvers. In this approach we specify what "states of computation" are, and which transitions between states are allowed. In this way, we define a directed graph such that every execution of a procedure corresponds to a path in this graph. This allows us to model algorithms of answer set solvers by a mathematically simple and elegant object, graph, rather than a collection of pseudocode statements. We use this abstract framework to describe and prove the correctness of the answer set solver Smodels, and also of Smodelscc, which enhances the former using learning and backjumping techniques. Answer sets of a tight program can be found by running a SAT solver on the program's completion, because for such a program answer sets are in a one-to-one correspondence with models of completion. SAT is one of the most widely studied problems in computational logic, and many efficient SAT procedures were developed over the last decade. Using SAT solvers for computing answer sets allows us to take advantage of the advances in the SAT area. For a nontight program it is still the case that each answer set corresponds to a model of program's completion but not vice versa. We show how to modify the search method typically used in SAT solvers to allow testing models of completion and employ learning to utilize testing information to guide the search. We develop a new SAT-based answer set solver, called Cmodels, based on this idea. We develop an abstract graph based framework for describing SAT-based answer set solvers and use it to represent the Cmodels algorithm and to demonstrate its correctness. Such representations allow us to better understand similarities and differences between native and SAT-based answer set solvers. We formally compare the Smodels algorithm with a variant of the Cmodels algorithm without learning. Abstract frameworks for describing native and SAT-based answer set solvers facilitate the development of new systems. We propose and implement the answer set solver called SUP that can be seen as a combination of computational ideas behind Cmodels and Smodels. Like Cmodels, solver SUP operates by computing a sequence of models of completion of the given program, but it does not form the completion. Instead, SUP runs the Atleast algorithm, one of the main building blocks of the Smodels procedure. Both systems Cmodels and SUP, developed in this dissertation, proved to be competitive answer set programming systems. / text

Knowledge representation and search are two fundamental areas of artificial intelligence. Knowledge representation is the area of artificial intelligence which deals with capturing, in a formal language, the properties of objects and the relationships between objects. Search is a systematic examination of all possible candidate solutions to a problem that is described as a theory in some knowledge representation formalism. We compare traditional declarative programming formalisms such as PROLOG and DATALOG with answer-set programming formalisms such as logic programming with stable model semantic. In this thesis we develop an answer-set formalism we can DC. The logic of DC is based on the logic of prepositional schemata and a version of Closed World Assumption. Two important features of the DC logic is that it supports modeling of the cardinalities of sets and Horn clauses. These two features facilitate modeling of search problems. The DC system includes and implementation of a grounder and a solver. The grounder for the DC system grounds instances of problems retaining the structure of the cardinality of sets. The resulting theories are thus more concise. In addition, the solver for the DC system utilizes the structure of cardinality of sets to perform more efficient search. The second feature, Horn clauses, are used when transitive closure will eliminate the need for additional variables. The semantics of the Horn clauses are retained in the grounded theories. This also results in more concise theories. Our goal in developing DC is to provide the computer science community with a system which facilitates modeling of problems, is easy to use, is efficient and captures the class of problems in NP-search. We show experimental results comparing DC to other systems. These results show that DC is always competitive with state-of-the-art answer-set programming systems and for many problems DC is more efficient.

Décrypter le fonctionnement des réseaux biologiques est une des missions centrales de la biologie des systèmes. En particulier, les réseaux de transduction du signal sont essentiels pour la compréhension de la réponse cellulaire à des perturbations externes ou internes. Pour faire face à la complexité de ces réseaux, des modélisations aussi bien numériques que formelles sont nécessaires. Nous proposons un cadre de modélisation formelle, dans le cadre de réseaux logiques, afin d'obtenir des prédictions robustes sur le comportement et le contrôle des voies de signalisation. Nous modélisons la réponse des réseaux logiques de signalisation par du raisonnement automatique à l'aide de Programmation par Ensembles-Réponses (Answer Set Programming, ASP). ASP fournit un langage déclaratif pour la modélisation de divers problèmes de représentation des connaissances et de raisonnement. Des solveurs permettent plusieurs modes de raisonnement pour étudier la multitude d'ensembles réponses. En s'appuyant sur la richesse du langage de modélisation et ses capacités de résolution très efficaces, nous utilisons ASP pour modéliser et résoudre trois problèmes dans le contexte des réseaux logiques de signalisation: apprentissage de réseaux booléens, calculs de plan d'expériences, et l'identification des contrôleurs. Globalement, la contribution de cette thèse est de trois ordres. Premièrement, nous introduisons un cadre formel pour la caractérisation et le raisonnement sur la réponse des réseaux logiques de signalisation. Deuxièmement, nous contribuons à une liste croissante d'applications réussies d'ASP en biologie des systèmes. Troisièmement, nous présentons un logiciel fournissant un pipeline complet de raisonnement automatisé sur la réponse des réseaux logiques de signalisation. / Deciphering the functioning of biological networks is one of the central tasks in systems biology. In particular, signal transduction networks are crucial for the understanding of the cellular response to external and internal perturbations. Importantly, in order to cope with the complexity of these networks, mathematical and computational modeling is required. We propose a computational modeling framework in order to achieve more robust discoveries in the context of logical signaling networks. More precisely, we focus on modeling the response of logical signaling networks by means of automated reasoning using Answer Set Programming (ASP). ASP provides a declarative language for modeling various knowledge representation and reasoning problems. Moreover, available ASP solvers provide several reasoning modes for assessing the multitude of answer sets. Therefore, leveraging its rich modeling language and its highly efficient solving capacities, we use ASP to address three challenging problems in the context of logical signaling networks: learning of (Boolean) logical networks, experimental design, and identification of intervention strategies. Overall, the contribution of this thesis is three-fold. Firstly, we introduce a mathematical framework for characterizing and reasoning on the response of logical signaling networks. Secondly, we contribute to a growing list of successful applications of ASP in systems biology. Thirdly, we present a software providing a complete pipeline for automated reasoning on the response of logical signaling networks.

abstract: Knowledge Representation (KR) is one of the prominent approaches to Artificial Intelligence (AI) that is concerned with representing knowledge in a form that computer systems can utilize to solve complex problems. Answer Set Programming (ASP), based on the stable model semantics, is a widely-used KR framework that facilitates elegant and efficient representations for many problem domains that require complex reasoning. However, while ASP is effective on deterministic problem domains, it is not suitable for applications involving quantitative uncertainty, for example, those that require probabilistic reasoning. Furthermore, it is hard to utilize information that can be statistically induced from data with ASP problem modeling. This dissertation presents the language LP^MLN, which is a probabilistic extension of the stable model semantics with the concept of weighted rules, inspired by Markov Logic. An LP^MLN program defines a probability distribution over "soft" stable models, which may not satisfy all rules, but the more rules with the bigger weights they satisfy, the bigger their probabilities. LP^MLN takes advantage of both ASP and Markov Logic in a single framework, allowing representation of problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way. This dissertation establishes formal relations between LP^MLN and several other formalisms, discusses inference and weight learning algorithms under LP^MLN, and presents systems implementing the algorithms. LP^MLN systems can be used to compute other languages translatable into LP^MLN. The advantage of LP^MLN for probabilistic reasoning is illustrated by a probabilistic extension of the action language BC+, called pBC+, defined as a high-level notation of LP^MLN for describing transition systems. Various probabilistic reasoning about transition systems, especially probabilistic diagnosis, can be modeled in pBC+ and computed using LP^MLN systems. pBC+ is further extended with the notion of utility, through a decision-theoretic extension of LP^MLN, and related with Markov Decision Process (MDP) in terms of policy optimization problems. pBC+ can be used to represent (PO)MDP in a succinct and elaboration tolerant way, which enables planning with (PO)MDP algorithms in action domains whose description requires rich KR constructs, such as recursive definitions and indirect effects of actions. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2019

In the last decade, Answer Set Programming (ASP) and Satisfiability (SAT) have been used to solve combinatorial search problems and practical applications in which they arise. In each of these formalisms, a tool called a solver is used to solve problems. A solver takes as input a specification of the problem – a logic program in the case of ASP, and a CNF theory for SAT – and produces as output a solution to the problem. Designing fast solvers is important for the success of this general-purpose approach to solving search problems. Classes of instances that pose challenges to solvers can help in this task. In this dissertation we create challenging yet simple benchmarks for existing solvers in ASP and SAT.We do so by providing models of simple logic programs as well as models of simple CNF theories. We then randomly generate logic programs as well as CNF theories from these models. Our experimental results show that computing answer sets of random logic programs as well as models of random CNF theories with carefully chosen parameters is hard for existing solvers. We generate random logic programs with 2-literals, and our experiments show that it is hard for ASP solvers to obtain answer sets of purely negative and constraint-free programs, indicating the importance of these programs in the development of ASP solvers. An easy-hard-easy pattern emerges as we compute the average number of choice points generated by ASP solvers on randomly generated 2-literal programs with an increasing number of rules. We provide an explanation for the emergence of this pattern in these programs. We also theoretically study the probability of existence of an answer set for sparse and dense 2-literal programs. We consider simple classes of mixed Horn formulas with purely positive 2- literal clauses and purely negated Horn clauses. First we consider a class of mixed Horn formulas wherein each formula has m 2-literal clauses and k-literal negated Horn clauses. We show that formulas that are generated from the phase transition region of this class are hard for complete SAT solvers. The second class of Mixed Horn Formulas we consider are obtained from completion of a certain class of random logic programs. We show the appearance of an easy-hard-easy pattern as we generate formulas from this class with increasing numbers of clauses, and that the formulas generated in the hard region can be used as benchmarks for testing incomplete SAT solvers.

Deciphering the functioning of biological networks is one of the central tasks in systems biology. In particular, signal transduction networks are crucial for the understanding of the cellular response to external and internal perturbations. Importantly, in order to cope with the complexity of these networks, mathematical and computational modeling is required. We propose a computational modeling framework in order to achieve more robust discoveries in the context of logical signaling networks. More precisely, we focus on modeling the response of logical signaling networks by means of automated reasoning using Answer Set Programming (ASP). ASP provides a declarative language for modeling various knowledge representation and reasoning problems. Moreover, available ASP solvers provide several reasoning modes for assessing the multitude of answer sets. Therefore, leveraging its rich modeling language and its highly efficient solving capacities, we use ASP to address three challenging problems in the context of logical signaling networks: learning of (Boolean) logical networks, experimental design, and identification of intervention strategies. Overall, the contribution of this thesis is three-fold. Firstly, we introduce a mathematical framework for characterizing and reasoning on the response of logical signaling networks. Secondly, we contribute to a growing list of successful applications of ASP in systems biology. Thirdly, we present a software providing a complete pipeline for automated reasoning on the response of logical signaling networks. / Deciphering the functioning of biological networks is one of the central tasks in systems biology. In particular, signal transduction networks are crucial for the understanding of the cellular response to external and internal perturbations. Importantly, in order to cope with the complexity of these networks, mathematical and computational modeling is required. We propose a computational modeling framework in order to achieve more robust discoveries in the context of logical signaling networks. More precisely, we focus on modeling the response of logical signaling networks by means of automated reasoning using Answer Set Programming (ASP). ASP provides a declarative language for modeling various knowledge representation and reasoning problems. Moreover, available ASP solvers provide several reasoning modes for assessing the multitude of answer sets. Therefore, leveraging its rich modeling language and its highly efficient solving capacities, we use ASP to address three challenging problems in the context of logical signaling networks: learning of (Boolean) logical networks, experimental design, and identification of intervention strategies. Overall, the contribution of this thesis is three-fold. Firstly, we introduce a mathematical framework for characterizing and reasoning on the response of logical signaling networks. Secondly, we contribute to a growing list of successful applications of ASP in systems biology. Thirdly, we present a software providing a complete pipeline for automated reasoning on the response of logical signaling networks.