Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

Combining open and closed world reasoning for the semantic web

Dissertação para obtenção do Grau de Doutor em InformáticaOne important problem in the ongoing standardization of knowledge representation languages for the Semantic Web is combining open world ontology languages, such as the OWL-based ones, and closed world rule-based languages. The main difficulty of such a combination is that both formalisms are quite orthogonal w.r.t. expressiveness and how decidability is achieved. Combining non-monotonic rules and ontologies is thus a challenging task that requires careful balancing between expressiveness of the knowledge representation language and the computational complexity of reasoning. In this thesis, we will argue in favor of a combination of ontologies and nonmonotonic rules that tightly integrates the two formalisms involved, that has a computational complexity that is as low as possible, and that allows us to query for information instead of calculating the whole model. As our starting point we choose the mature approach of hybrid MKNF knowledge bases, which is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. We extend the two-valued framework of MKNF logics to a three-valued logics, and we propose a well-founded semantics for non-disjunctive hybrid MKNF knowledge bases. This new semantics promises to provide better efficiency of reasoning,and it is faithful w.r.t. the original two-valued MKNF semantics and compatible with both the OWL-based semantics and the traditional Well- Founded Semantics for logic programs. We provide an algorithm based on operators to compute the unique model, and we extend SLG resolution with tabling to a general framework that allows us to query a combination of non-monotonic rules and any given ontology language. Finally, we investigate concrete instances of that procedure w.r.t. three tractable ontology languages, namely the three description logics underlying the OWL 2 pro les.Fundação para a Ciência e Tecnologia - grant contract SFRH/BD/28745/200

A Language for Inconsistency-Tolerant Ontology Mapping

Ontology alignment plays a key role in enabling interoperability among various data sources present in the web. The nature of the world is such, that the same concepts differ in meaning, often so slightly, which makes it difficult to relate these concepts. It is the omni-present heterogeneity that is at the core of the web. The research work presented in this dissertation, is driven by the goal of providing a robust ontology alignment language for the semantic web, as we show that description logics based alignment languages are not suitable for aligning ontologies. The adoption of the semantic web technologies has been consistently on the rise over the past decade, and it continues to show promise. The core component of the semantic web is the set of knowledge representation languages -- mainly the W3C (World Wide Web Consortium) standards Web Ontology Language (OWL), Resource Description Framework (RDF), and Rule Interchange Format (RIF). While these languages have been designed in order to be suitable for the openness and extensibility of the web, they lack certain features which we try to address in this dissertation. One such missing component is the lack of non-monotonic features, in the knowledge representation languages, that enable us to perform common sense reasoning. For example, OWL supports the open world assumption (OWA), which means that knowledge about everything is assumed to be possibly incomplete at any point of time. However, experience has shown that there are situations that require us to assume that certain parts of the knowledge base are complete. Employing the Closed World Assumption (CWA) helps us achieve this. Circumscription is a very well-known approach towards CWA, which provides closed world semantics by employing the idea of minimal models with respect to certain predicates which are closed. We provide the formal semantics of the notion of Grounded Circumscription, which is an extension of circumscription with desirable properties like decidability. We also provide a tableaux calculus to reason over knowledge bases under the notion of grounded circumscription. Another form of common sense logic, is default logic. Default logic provides a way to specify rules that, by default, hold in most cases but not necessarily in all cases. The classic example of such a rule is: If something is a bird then it flies. The power of defaults comes from the ability of the logic to handle exceptions to the default rules. For example, a bird will be assumed to fly by default unless it is an exception, i.e. it belongs to a class of birds that do not fly, like penguins. Interestingly, this property of defaults can be utilized to create mappings between concepts of different ontologies (knowledge bases). We provide a new semantics for the integration of defaults in description logics and show that it improves upon previously known results in literature. In this study, we give various examples to show the utility and advantages of using a default logic based ontology alignment language. We provide the semantics and decidability results of a default based mapping language for tractable fragments of description logics (or OWL). Furthermore, we provide a proof of concept system and qualitative analysis of the results obtained from the system when compared to that of traditional mapping repair techniques

Causative alternation licensing in Urdu: An event structure account

Given the central role of the verb in clause structure, it is vital to understand the properties of the SEMANTIC ROOT and the EVENT SCHEMA, two constituent aspects of verb meaning, in order to understand how lexical semantic categories relate to syntactic categories. The nature of the interface between these components can, in turn, reveal the overall design of language. However, the main challenge is to make precise the nature of the semantic root and event schema, and their interactive role in argument realization options. To address this challenge, empirical evidence from diverse languages is required to determine how argument realization can be universally accounted for in terms of semantic root and event schema-based lexical semantic representation. The primary purpose of this study is to explicate the roles of semantic root and event schema in Urdu change-of-state (COS) verbs’ causative alternation, formulating licensing conditions on the lexical semantics-syntax interface involved in the phenomenon. On the semantic side of the interface, the argumentation is framed within Rappaport-Hovav and Levin’s (1998a) event structure account, and on the syntactic side, the study assumes Culicover and Jackendoff’s (2005) Simpler Syntax which accounts for an alternation in terms of constraint-based interface principles. Given that the adequacy of theory is bound up with the reliability of empirical evidence, this study is based on data from multiple sources (lexical translation, Urdu WordNet, Urdu Lughat, individual and dialogical introspection, and speaker survey), conducts extensive analysis of morphosemantic as well as morphosyntactic aspects of 112 Urdu COS verbs, and shows that the causative alternation results from an interaction of multiple licensing factors. The study reaches the following conclusions: (a) The anticausative form of a COS verb is basic and causative forms are derived. (b) The causative derivation shows gradient and dynamic productivity, and an interaction between lexical schemas and morphological operations, marking the CAUSE relation which reflects causal responsibility between the event participants. (c) An anticausative lexicalizes both manner and result, with a [BECOME [Y ]] event structure. (d) An anticausative’s event schema and root license only the patient argument; any additional argument is licensed by the root. The cause arguments in causatives are introduced by causative operations, and are obligatorily event schema participants. The syntactic realization of semantic arguments is sensitive to the causal responsibility relation which is reflected in the predicate’s event structure through the primitive predicate CAUSE and its relation with ACT and BECOME. (e) The various aspects of Urdu COS verbs’ causative alternation lead us to the linking rules which show that the argument structure reflects the semantics it inherits from its semantic sources of roots and event schema. Overall the study shows that the event structure account of Urdu COS verbs’ causative alternation supports the decomposition of the grammar into independent generative components that interact through interface rules. The bottom line is that such a syntax-semantics interface formulation of alternation avoids syntactic complexity

Individual Differences in Function Learning as They Relate to the Learning of Conceptual Information

Individual differences have not often been considered within the problem-solving or concept-learning literatures despite the indication that some individuals are better able to transfer to novel problems and that manipulations in strategy can effectively increase the ability to transfer: Gick & Holyoak, 1983). Research in the function-learning domain indicates that there may be two qualitatively different types of learners: those who remember distinct example associations: exemplar learners) and others who abstract rules that govern each association: rule learners; DeLosh, Busemeyer, & McDaniel, 1997). Data from two unpublished studies: McDaniel, Cahill, Robbins, & Trumpower, 2012; Fadler, Lee, Scullin, Shelton, & McDaniel, 2012) have demonstrated the stability of these two types of learning across a variety of different higher order problem-solving, concept-learning, and cognitive tasks. However, it remains to be seen whether these differences between learners have implications for the type of conceptual material often used in classrooms. In the current project, this issue was addressed through two experiments. During Experiment 1, participants were first identified as exemplar or rule-based learners on the basis of function learning transfer performance. Each group then read several passages and answered questions about the passages that ranged in their degree of transfer. Rule learners performed better than exemplar learners on each question type and the two types of learners also demonstrated qualitatively different processing during function learning training and on a test of analogical transfer. The data from Experiment 2 showed that rule learners behaved qualitatively differently from exemplar learners during function learning training but failed to replicate the passage data from Experiment 1. However, a benefit was found on recognition memory for exemplar learners on a concept-learning task. The current study is the first to show differential benefits for exemplar and rule-based processing. It also provides evidence that function-learning tendency can be used to predict differences on concept-learning tasks and that only rule learning is associated with abstraction ability. The findings suggest that individual differences should be considered both in current hybrid models of categorization, but also potentially in classrooms that might rely heavily on problem solving, where the differences in types of learners may have an impact on student performance and understanding

Towards a complete multiple-mechanism account of predictive language processing [Commentary on Pickering & Garrod]

Although we agree with Pickering & Garrod (P&G) that prediction-by-simulation and prediction-by-association are important mechanisms of anticipatory language processing, this commentary suggests that they: (1) overlook other potential mechanisms that might underlie prediction in language processing, (2) overestimate the importance of prediction-by-association in early childhood, and (3) underestimate the complexity and significance of several factors that might mediate prediction during language processing