Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

The COPLE2 Corpus: a Learner Corpus for Portuguese

We present the COPLE2 corpus, a learner corpus of Portuguese that includes written and spoken texts produced by learners of Portuguese as a second or foreign language. The corpus includes at the moment a total of 182,474 tokens and 978 texts, classified according to the CEFR scales. The original handwritten productions are transcribed in TEI compliant XML format and keep record of all the original information, such as reformulations, insertions and corrections made by the teacher, while the recordings are transcribed and aligned with EXMARaLDA. The TEITOK environment enables different views of the same document (XML, student version, corrected version), a CQP-based search interface, the POS, lemmatization and normalization of the tokens, and will soon be used for error annotation in stand-off format. The corpus has already been a source of data for phonological, lexical and syntactic interlanguage studies and will be used for a data-informed selection of language features for each proficiency level.info:eu-repo/semantics/publishedVersio

Towards automated knowledge-based mapping between individual conceptualisations to empower personalisation of Geospatial Semantic Web

Geospatial domain is characterised by vagueness, especially in the semantic disambiguation of the concepts in the domain, which makes defining universally accepted geo- ontology an onerous task. This is compounded by the lack of appropriate methods and techniques where the individual semantic conceptualisations can be captured and compared to each other. With multiple user conceptualisations, efforts towards a reliable Geospatial Semantic Web, therefore, require personalisation where user diversity can be incorporated. The work presented in this paper is part of our ongoing research on applying commonsense reasoning to elicit and maintain models that represent users' conceptualisations. Such user models will enable taking into account the users' perspective of the real world and will empower personalisation algorithms for the Semantic Web. Intelligent information processing over the Semantic Web can be achieved if different conceptualisations can be integrated in a semantic environment and mismatches between different conceptualisations can be outlined. In this paper, a formal approach for detecting mismatches between a user's and an expert's conceptual model is outlined. The formalisation is used as the basis to develop algorithms to compare models defined in OWL. The algorithms are illustrated in a geographical domain using concepts from the SPACE ontology developed as part of the SWEET suite of ontologies for the Semantic Web by NASA, and are evaluated by comparing test cases of possible user misconceptions

A Brief History of Updates of Answer-Set Programs

Funding Information: The authors would like to thank José Alferes, Martin Baláz, Federico Banti, Antonio Brogi, Martin Homola, Luís Moniz Pereira, Halina Przymusinska, Teodor C. Przymusinski, and Theresa Swift, with whom they worked on the topic of this paper over the years, as well as Ricardo Gonçalves and Matthias Knorr for valuable comments on an earlier draft of this paper. The authors would also like to thank the anonymous reviewers for their insightful comments and suggestions, which greatly helped us improve this paper. The authors were partially supported by Fundação para a Ciência e Tecnologia through projects FORGET (PTDC/CCI-INF/32219/2017) and RIVER (PTDC/CCI-COM/30952/2017), and strategic project NOVA LINCS (UIDB/04516/2020). Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press.Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper, we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.publishersversionpublishe

Modularity in answer set programs

Answer set programming (ASP) is an approach to rule-based constraint programming allowing flexible knowledge representation in variety of application areas. The declarative nature of ASP is reflected in problem solving. First, a programmer writes down a logic program the answer sets of which correspond to the solutions of the problem. The answer sets of the program are then computed using a special purpose search engine, an ASP solver. The development of efficient ASP solvers has enabled the use of answer set programming in various application domains such as planning, product configuration, computer aided verification, and bioinformatics. The topic of this thesis is modularity in answer set programming. While modern programming languages typically provide means to exploit modularity in a number of ways to govern the complexity of programs and their development process, relatively little attention has been paid to modularity in ASP. When designing a module architecture for ASP, it is essential to establish full compositionality of the semantics with respect to the module system. A balance is sought between introducing restrictions that guarantee the compositionality of the semantics and enforce a good programming style in ASP, and avoiding restrictions on the module hierarchy for the sake of flexibility of knowledge representation. To justify a replacement of a module with another, that is, to be able to guarantee that changes made on the level of modules do not alter the semantics of the program when seen as an entity, a notion of equivalence for modules is provided. In close connection with the development of the compositional module architecture, a transformation from verification of equivalence to search for answer sets is developed. The translation-based approach makes it unnecessary to develop a dedicated tool for the equivalence verification task by allowing the direct use of existing ASP solvers. Translations and transformations between different problems, program classes, and formalisms are another central theme in the thesis. To guarantee efficiency and soundness of the translation-based approach, certain syntactical and semantical properties of transformations are desirable, in terms of translation time, solution correspondence between the original and the transformed problem, and locality/globality of a particular transformation. In certain cases a more refined notion of minimality than that inherent in ASP can make program encodings more intuitive. Lifschitz' parallel and prioritized circumscription offer a solution in which certain atoms are allowed to vary or to have fixed values while others are falsified as far as possible according to priority classes. In this thesis a linear and faithful transformation embedding parallel and prioritized circumscription into ASP is provided. This enhances the knowledge representation capabilities of answer set programming by allowing the use of existing ASP solvers for computing parallel and prioritized circumscription

Improving PARMA Trailing

Taylor introduced a variable binding scheme for logic variables in his PARMA system, that uses cycles of bindings rather than the linear chains of bindings used in the standard WAM representation. Both the HAL and dProlog languages make use of the PARMA representation in their Herbrand constraint solvers. Unfortunately, PARMA's trailing scheme is considerably more expensive in both time and space consumption. The aim of this paper is to present several techniques that lower the cost. First, we introduce a trailing analysis for HAL using the classic PARMA trailing scheme that detects and eliminates unnecessary trailings. The analysis, whose accuracy comes from HAL's determinism and mode declarations, has been integrated in the HAL compiler and is shown to produce space improvements as well as speed improvements. Second, we explain how to modify the classic PARMA trailing scheme to halve its trailing cost. This technique is illustrated and evaluated both in the context of dProlog and HAL. Finally, we explain the modifications needed by the trailing analysis in order to be combined with our modified PARMA trailing scheme. Empirical evidence shows that the combination is more effective than any of the techniques when used in isolation. To appear in Theory and Practice of Logic Programming.Comment: 36 pages, 7 figures, 8 table

Temporal reasoning in a logic programming language with modularity

Actualmente os Sistemas de Informação Organizacionais (SIO) lidam cada vez mais com informação que tem dependências temporais. Neste trabalho concebemos um ambiente de trabalho para construir e manter SIO Temporais. Este ambiente assenta sobre um linguagem lógica denominada Temporal Contextua) Logic Programming que integra modularidade com raciocínio temporal fazendo com que a utilização de um módulo dependa do tempo do contexto. Esta linguagem é a evolução de uma outra, também introduzida nesta tese, que combina Contextua) Logic Programming com Temporal Annotated Constraint Logic Programming, na qual a modularidade e o tempo são características ortogonais. Ambas as linguagens são formalmente discutidas e exemplificadas. As principais contribuições do trabalho descrito nesta tese incluem: • Optimização de Contextua) Logic Programming (CxLP) através de interpretação abstracta. • Sintaxe e semântica operacional para uma linguagem que combina de um modo independente as linguagens Temporal Annotated Constraint Logic Programming (TACLP) e CxLP. É apresentado um compilador para esta linguagem. • Linguagem (sintaxe e semântica) que integra de um modo inovador modularidade (CxLP) com raciocínio temporal (TACLP). Nesta linguagem a utilização de um dado módulo está dependente do tempo do contexto. É descrito um interpretador e um compilador para esta linguagem. • Ambiente de trabalho para construir e fazer a manutenção de SIO Temporais. Assenta sobre uma especificação revista da linguagem ISCO, adicionando classes e manipulação de dados temporais. É fornecido um compilador em que a linguagem resultante é a descrita no item anterior. ABSTRACT- Current Organisational Information Systems (OIS) deal with more and more Infor-mation that, is time dependent. In this work we provide a framework to construct and maintain Temporal OIS. This framework builds upon a logical language called Temporal Contextual. Logic Programming that deeply integrates modularity with tem-poral reasoning making the usage of a module time dependent. This language is an evolution of another one, also introduced in this thesis, that combines Contextual Logic Programming with Temporal Annotated Constraint Logic Programming where modularity and time are orthogonal features. Both languages are formally discussed and illustrated. The main contributions of the work described in this thesis include: • Optimisation of Contextual Logic Programming (CxLP) through abstract interpretation. • Syntax and operational semantics for an independent combination of the temporal framework Temporal Annotated Constraint Logic Programming (TACLP) and CxLP. A compiler for this language is also provided. • Language (syntax and semantics) that integrates in a innovative way modularity (CxLP) with temporal reasoning (TACLP). In this language the usage of a given module depends of the time of the context. An interpreter and a compiler for this language are described. • Framework to construct and maintain Temporal Organisational Information Systems. It builds upon a revised specification of the language ISCO, adding temporal classes and temporal data manipulation. A compiler targeting the language presented in the previous item is also given