The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined in terms of a $p$-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints

On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities for knowledge representation and reasoning

Improving approximation of domain-focused, corpus-based, lexical semantic relatedness

Semantic relatedness is a measure that quantifies the strength of a semantic link between two concepts. Often, it can be efficiently approximated with methods that operate on words, which represent these concepts. Approximating semantic relatedness between texts and concepts represented by these texts is an important part of many text and knowledge processing tasks of crucial importance in many domain-specific scenarios. The problem of most state-of-the-art methods for calculating domain-specific semantic relatedness is their dependence on highly specialized, structured knowledge resources, which makes these methods poorly adaptable for many usage scenarios. On the other hand, the domain knowledge in the fields such as Life Sciences has become more and more accessible, but mostly in its unstructured form - as texts in large document collections, which makes its use more challenging for automated processing. In this dissertation, three new corpus-based methods for approximating domain-specific textual semantic relatedness are presented and evaluated with a set of standard benchmarks focused on the field of biomedicine. Nonetheless, the proposed measures are general enough to be adapted to other domain-focused scenarios. The evaluation involves comparisons with other relevant state-of-the-art measures for calculating semantic relatedness and the results suggest that the methods presented here perform comparably or better than other approaches. Additionally, the dissertation also presents an experiment, in which one of the proposed methods is applied within an ontology matching system, DisMatch. The performance of the system was evaluated externally on a biomedically themed ‘Phenotype’ track of the Ontology Alignment Evaluation Initiative 2016 campaign. The results of the track indicate, that the use distributional semantic relatedness for ontology matching is promising, as the system presented in this thesis did stand out in detecting correct mappings that were not detected by any other systems participating in the track. The work presented in the dissertation indicates an improvement achieved w.r.t. the stat-of-the-art through the domain adapted use of the distributional principle (i.e. the presented methods are corpus-based and do not require additional resources). The ontology matching experiment showcases practical implications of the presented theoretical body of work

SimLex-999: Evaluating Semantic Models with (Genuine) Similarity Estimation

We present SimLex-999, a gold standard resource for evaluating distributional semantic models that improves on existing resources in several important ways. First, in contrast to gold standards such as WordSim-353 and MEN, it explicitly quantifies similarity rather than association or relatedness, so that pairs of entities that are associated but not actually similar [Freud, psychology] have a low rating. We show that, via this focus on similarity, SimLex-999 incentivizes the development of models with a different, and arguably wider range of applications than those which reflect conceptual association. Second, SimLex-999 contains a range of concrete and abstract adjective, noun and verb pairs, together with an independent rating of concreteness and (free) association strength for each pair. This diversity enables fine-grained analyses of the performance of models on concepts of different types, and consequently greater insight into how architectures can be improved. Further, unlike existing gold standard evaluations, for which automatic approaches have reached or surpassed the inter-annotator agreement ceiling, state-of-the-art models perform well below this ceiling on SimLex-999. There is therefore plenty of scope for SimLex-999 to quantify future improvements to distributional semantic models, guiding the development of the next generation of representation-learning architectures