abstract: Natural Language Processing is a subject that combines computer science and linguistics, aiming to provide computers with the ability to understand natural language and to develop a more intuitive human-computer interaction. The research community has developed ways to translate natural language to mathematical formalisms. It has not yet been shown, however, how to automatically translate different kinds of knowledge in English to distinct formal languages. Most of the recent work presents the problem that the translation method aims to a specific formal language or is hard to generalize. In this research, I take a first step to overcome this difficulty and present two algorithms which take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F. The expression F returned by the first algorithm satisfies F@G=H and, in the case of the second algorithm, we obtain G@F=H. The lambda expressions represent the meanings of words and sentences. For each formal language that one desires to use with the algorithms, the language must be defined in terms of lambda calculus. Also, some additional concepts must be included. After doing this, given a sentence, its representation and knowing the representation of several words in the sentence, the algorithms can be used to obtain the representation of the other words in that sentence. In this work, I define two languages and show examples of their use with the algorithms. The algorithms are illustrated along with soundness and completeness proofs, the latter with respect to typed lambda-calculus formulas up to the second order. These algorithms are a core part of a natural language semantics system that translates sentences from English to formulas in different formal languages. / Dissertation/Thesis / M.S. Computer Science 2010

abstract: Action language C+ is a formalism for describing properties of actions, which is based on nonmonotonic causal logic. The definite fragment of C+ is implemented in the Causal Calculator (CCalc), which is based on the reduction of nonmonotonic causal logic to propositional logic. This thesis describes the language of CCalc in terms of answer set programming (ASP), based on the translation of nonmonotonic causal logic to formulas under the stable model semantics. I designed a standard library which describes the constructs of the input language of CCalc in terms of ASP, allowing a simple modular method to represent CCalc input programs in the language of ASP. Using the combination of system F2LP and answer set solvers, this method achieves functionality close to that of CCalc while taking advantage of answer set solvers to yield efficient computation that is orders of magnitude faster than CCalc for many benchmark examples. In support of this, I created an automated translation system Cplus2ASP that implements the translation and encoding method and automatically invokes the necessary software to solve the translated input programs. / Dissertation/Thesis / M.S. Computer Science 2011

Les ontologies sont utilisées pour la représentation et l’interrogation de connaissances d’un domaine précis et peuvent être représentées en partie à l’aide des logiques de description légères. Ces ontologies peuvent être issues de plusieurs sources dont les données sont plus ou moins complétés, ainsi certaines données peuvent être incomplètes ou incohérentes empêchant la déduction d’autres données. L’Answer Set Programming (ASP) est un langage de programmation logique non-monotone à base de règles permettant de représenter des données incomplètes mais il ne permet pas de représenter les logiques de description légères. Les règles existentielles généralisent les logiques de description légères et forment aussi un langage de programmation logique mais ne permettant pas la définition d’exceptions. A partir d’une étude théorique d’ASP et des règles existentielles nous proposons de regrouper en un seul formalisme ces deux langages, nous définissons le formalisme des programmes non-monotones existentiels permettant de traiter un programme provenant d’une ontologie avec exceptions. Cette extension a pour but de généraliser à la fois ASP et les règles existentielles et d’utiliser la puissance des solveurs ASP pour raisonner sur des ontologies avec exceptions. Cette étude propose d’approfondir les travaux sur la décidabilité d’un programme avec l’extension aux programmes non-monotones existentiels. Nous proposons aussi d’améliorer les résultats lies à l’interrogation d’un programme ASP ainsi qu’une implémentation d’une extension du solveur ASPeRiX pour traiter les programmes non-monotones existentiels. / Ontologies are meant to represent or to queryknowledge from a precise domain and can berepresented, in part, by logic formalisms such thatdescription logics. These ontologies can be providedby several sources where knowledge is more or lesscomplete, hence some data can be incomplete orincoherent preventing the deduction of other data.Answer Set Programming (ASP) formalism is anon-monotonic logic programming language based onrules, often used in knowledge representation, whichhas the feature to represent incomplete data.However, it’s impossible to represent lite descriptionlogics in ASP, because of existential variables in rules.Existential rules generalize lite description logics andalso form a programmation logic language that butdoesn’t offer the possibility to represent exceptions.Based on a theoritical study of ASP and existentialrules, we propose to gather both languages in aunique formalism, we define non-monotonic existentialprogram allowing to deal with ontology withexceptions. This extension aims to generalize bothASP and existential rules program and to use theefficiency of ASP solvers to reason on ontologies withexceptions. This thesis propose to deepen worksabout entailment and decidability of a non-monotonicexistential program. Another result from this study isthe improvement of interrogation in ASP and theimplementation of an extension of the ASPeRiX solverto deal with non-monotonic existential programs.

abstract: Knowledge representation and reasoning is a prominent subject of study within the field of artificial intelligence that is concerned with the symbolic representation of knowledge in such a way to facilitate automated reasoning about this knowledge. Often in real-world domains, it is necessary to perform defeasible reasoning when representing default behaviors of systems. Answer Set Programming is a widely-used knowledge representation framework that is well-suited for such reasoning tasks and has been successfully applied to practical domains due to efficient computation through grounding--a process that replaces variables with variable-free terms--and propositional solvers similar to SAT solvers. However, some domains provide a challenge for grounding-based methods such as domains requiring reasoning about continuous time or resources. To address these domains, there have been several proposals to achieve efficiency through loose integrations with efficient declarative solvers such as constraint solvers or satisfiability modulo theories solvers. While these approaches successfully avoid substantial grounding, due to the loose integration, they are not suitable for performing defeasible reasoning on functions. As a result, this expressive reasoning on functions must either be performed using predicates to simulate the functions or in a way that is not elaboration tolerant. Neither compromise is reasonable; the former suffers from the grounding bottleneck when domains are large as is often the case in real-world domains while the latter necessitates encodings to be non-trivially modified for elaborations. This dissertation presents a novel framework called Answer Set Programming Modulo Theories (ASPMT) that is a tight integration of the stable model semantics and satisfiability modulo theories. This framework both supports defeasible reasoning about functions and alleviates the grounding bottleneck. Combining the strengths of Answer Set Programming and satisfiability modulo theories enables efficient continuous reasoning while still supporting rich reasoning features such as reasoning about defaults and reasoning in domains with incomplete knowledge. This framework is realized in two prototype implementations called MVSM and ASPMT2SMT, and the latter was recently incorporated into a non-monotonic spatial reasoning system. To define the semantics of this framework, we extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow "intensional functions" and provide analyses of the theoretical properties of this new formalism and on the relationships between this and existing approaches. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2016

abstract: Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on Boolean decision problems, it has difficulty in expressing quantitative uncertainty and probability in a natural way. Logic Programs under the answer set semantics and Markov Logic Network (LPMLN) is a recent extension of answer set programs to overcome the limitation of the deterministic nature of ASP by adopting the log-linear weight scheme of Markov Logic. This thesis investigates the relationships between LPMLN and two other extensions of ASP: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. The studied relationships show how different extensions of answer set programs are related to each other, and how they are related to formalisms in Statistical Relational Learning, such as Problog and MLN, which have shown to be closely related to LPMLN. The studied relationships compare the properties of the involved languages and provide ways to compute one language using an implementation of another language. This thesis first presents a translation of LPMLN into programs with weak constraints. The translation allows for computing the most probable stable models (i.e., MAP estimates) or probability distribution in LPMLN programs using standard ASP solvers so that the well-developed techniques in ASP can be utilized. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl’s Causal Models, that are shown to be translatable into LPMLN. This thesis also presents a translation of P-log into LPMLN. The translation tells how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers or MLN solvers. / Dissertation/Thesis / Masters Thesis Computer Science 2017

各式應用領域常會面臨許多撮合(Matching)問題，但當我們有需求時卻往往無法定出好的撮合策略，更遑論找到可實現此策略的電腦化解決方法。本研究希望針對穩定婚姻配對、大學聯考分發、論文審查分配、專題選修等等之類的撮合問題提供各種可行的通用撮合策略，可供使用者依其需求快速選用。而後續提供的支援系統則可據此產生一個以WEB為基礎的客製化專門應用領域撮合系統。 而什麼是撮合呢? 撮合是指有A、B兩群對象，在特定的規則與限制條件下，希望使每一A(B) 群對象可以連結至某些B(A)群對象，而使總體滿意度達到最大。以數學而言，一個A、B兩群間的撮合，就是一個滿足特定條件的A、B兩個集合間的二元關係。撮合類型可能是一對一、一對多、 多對多三種。一對一表示一個A群成員只能跟一個B群成員配對，一對多表示 一個A(B) 群成員能跟多個B(A) 群成員配對，多對多則指一個A群成員能跟多個B群成員配對且一個B群成員也能跟多個A群成員配對。 由於撮合型態與策略具有相當大的分歧性，以專用演算法實做並不實際，因此我們採用ASP(Answer set programming)實做撮合程式。ASP 是一種邏輯編程語言，具有宣告式程式特性，廣泛用於組合性問題的解決上，極適合應用在撮合策略的制定與實做。 在可真正執行撮合程式之前，必須預先建置A、B兩群對象的基本資料，因此我們的系統將允許開發者輸入A、B兩群對象的基本後設資料及撮合策略，而系統將據此建立對應Web介面與資料庫，允許使用者建立撮合對象的基本資料。一旦基本資料建立完成，系統即可依據系統設定的撮合策略以及以ASP實做的基本配對規則快速產生撮合結果，提供給使用者參考。 / There are a lot of application domains in which we may encounter the problem of finding a matching among two parties of entities. However, it is often the case that once a matching is needed, we cannot easily find a good matching strategy suitable for our purpose, not to mention one with a computerized implementation. This thesis aims to provide a web-based matching generation system allowing the quick generation of customized matching systems for users' need after their input of different demands of matching types and strategies. The supported types of matchings include most often used cases such as marriage/dating matching, paper review assignment, college admission dispatch and student-advisor selection etc. What is a matching? A (bipartite) matching problem contains two parties of entities, each member of which has a preference over members of the opposite party. A matching in a matching problem is a binary relation between both parties of entities. The goal of a matching problem is to find one or more optimal matching in which the total satisfaction of both party members is maximized. Matching problems can be classified according restrictions imposed on matchings. 1-1 matching requires each member of both parties to be matched to at most one opposite party member, 1-m matching allows only members of one party to be matched to more than one opposite party member, and m-m matching allows members of both parties to be matched to more than one opposite party member. Because there is a great variety of matching types and strategies, it is impractical to employ dedicated algorithm per case. It is thus eagerly expected to have a general framework in which different types of matching and strategies can be encoded. By applying Answer-set Programming (ASP) we provided one such framework in this thesis. ASP is logic programming language with declarative characteristics, widely applied in the solution of hard combinatorial problems, to be used in the encoding and solving of matching problems with different preference matching strategies. Theoretical discussion of matching algorithms always assumes that party members and their preferences are available in advance. However, to engineer a matching system, we still need to provide means to achieve it. Our system is thus also a matching support system, through the web interface of which developers and end-users can enter meta and individual information about all concerned properties and/or preferences of party members. After a possibly further processing of users' preference on the values of concerned properties of opposite party members for deriving every member's preference on the member of the opposite party, succeeding matching thus can obtain all needed data.

abstract: Modeling dynamic systems is an interesting problem in Knowledge Representation (KR) due to their usefulness in reasoning about real-world environments. In order to effectively do this, a number of different formalisms have been considered ranging from low-level languages, such as Answer Set Programming (ASP), to high-level action languages, such as C+ and BC. These languages show a lot of promise over many traditional approaches as they allow a developer to automate many tasks which require reasoning within dynamic environments in a succinct and elaboration tolerant manner. However, despite their strengths, they are still insufficient for modeling many systems, especially those of non-trivial scale or that require the ability to cope with exceptions which occur during execution, such as unexpected events or unintended consequences to actions which have been performed. In order to address these challenges, a theoretical framework is created which focuses on improving the feasibility of applying KR techniques to such problems. The framework is centered on the action language BC+, which integrates many of the strengths of existing KR formalisms, and provides the ability to perform efficient reasoning in an incremental fashion while handling exceptions which occur during execution. The result is a developer friendly formalism suitable for performing reasoning in an online environment. Finally, the newly enhanced Cplus2ASP 2 is introduced, which provides a number of improvements over the original version. These improvements include implementing BC+ among several additional languages, providing enhanced developer support, and exhibiting a significant performance increase over its predecessors and similar systems. / Dissertation/Thesis / M.S. Computer Science 2014

Planning is a challenging research area since the early days of Artificial Intelligence. The planning problem is the task of finding a sequence of actions leading an agent from a given initial state to a desired goal state. Whereas classical planning adopts restricting assumptions such as complete knowledge about the initial state and deterministic action effects, in real world scenarios we often have to face incomplete knowledge and non-determinism. Classical planning languages and algorithms do not take these facts into account. So, there is a strong need for formal languages describing such non-classical planning problems on the one hand and for (declarative) methods for solving these problems on the other hand.In this thesis, we present the action language Kc, which is based on flexible action languages from the knowledge representation community and extends these by useful concepts from logic programming.We define two basic semantics for this language which reflect optimistic and secure (i.e. sceptical) plans in presence of incomplete information or nondeterminism. These basic semantics are furthermore extended to planning with action costs, where each action can have an assigned cost value. Here, we address optimal plans as well as plans which stay within a certain overall cost limit.Next, we develop efficient (i.e. polynomial) transformations from planning problems described in our language Kc to disjunctive logic programs which are then evaluated under the so-called Answer Set Semantics. In this context, we introduce a general new method for problem solving in Answer Set Programming (ASP) which takes the genuine "guess and check" paradigm in ASP into account and allows us to integrate separate "guess" and "check" programs into a single logic program. Based on these methods, we have implemented the planning system DLVK. We discuss problem solving and knowledge representation in Kc using DLVK by means of several examples. The proposed methods and the DLVK system are also evaluated experimentally and compared against related approaches. Finally, we present a practical application scenario from the area of design and monitoring of multi-agent systems. As we will see, this monitoring approach is not restricted to our particular formalism. / Austrian Science Funds (FWF)

This thesis presents the Planning System DLVK, which supports the novel Planning Language K. The language allows to represent AI planning problems in a declarative way and is capable of representing incomplete knowledge as well as nondeterministic effects of actions.After explaining some basics, the syntax and semantics of this language will be formally described and some results on the computational complexity of our language will be given, proving that K is capable of expressing hard planning problems, possibly involving incomplete knowledge or uncertainty, such as secure (conformant) planning.A translation from various planning tasks specified in K to a logic programming framework will be shown subsequently. We have implemented a prototype of a planning system, DLVK, on top of the disjunctive logic programming system DLV, to show the practical use of our translation. This prototype will be presented in detail. Finally, examples and experimental results will be given, together with an outlook to further research. / Austrian Science Funds (FWF)

Este trabalho introduz uma técnica chamada Answer Set Programming Probabilístico (PASP), que permite a modelagem de teorias complexas e a verificação de sua consistência em relação a um conjunto de dados estatísticos. Propomos métodos de resolução baseados em uma redução para o problema da satisfazibilidade probabilística (PSAT) e um método de redução de Turing ao ASP. / This dissertation introduces a technique called Probabilistic Answer Set Programming (PASP), that allows modeling complex theories and check its consistence with respect to a set of statistical data. We propose a method of resolution based in the reduction to the probabilistic satisfiability problem (PSAT) and a Turing reduction method to ASP.