Relation-Changing Logics as Fragments of Hybrid Logics

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation. In general, these logics are undecidable, but we use our translations to identify decidable fragments. We also compare the expressive power of relation-changing modal logics with hybrid logics.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Completeness in hybrid type theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i in propositional and first-order hybrid logic. This means: interpret @iαa, where αa is an expression of any type a, as an expression of type a that rigidly returns the value that αa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual in hybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logic over Henkin’s logic.submittedVersionFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Blackburn, Patrick. University of Roskilde. Centre for Culture and Identity. Department of Philosophy and Science Studies; Dinamarca.Fil: Huertas, Antonia. Universitat Oberta de Catalunya; España.Fil: Manzano, María. Universidad de Salamanca; España.Ciencias de la Computació

Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

Axiomatizing hybrid xpath with data

In this paper we introduce sound and strongly complete axiomatizations for XPath with data constraints extended with hybrid operators. First, we present HXPath=, a multi-modal version of XPath with data, extended with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and we prove it is strongly complete with respect to the class of abstract data models, i.e., data models in which data values are abstracted as equivalence relations. We prove a general completeness result similar to the one presented in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system we introduce are also complete. The axiomatic systems that can be obtained in this way cover a large family of hybrid XPath languages over different classes of frames, for which we present concrete examples. In addition, we investigate axiomatizations over the class of tree models, structures widely used in practice. We show that a strongly complete, finitary, first-order axiomatization of hybrid XPath over trees does not exist, and we propose two alternatives to deal with this issue. We finally introduce filtrations to investigate the status of decidability of the satisfiability problem for these languages.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Conservative Extensions and Satisfiability in Fragments of First-Order Logic : Complexity and Expressive Power

In this thesis, we investigate the decidability and computational complexity of (deductive) conservative extensions in expressive fragments of first-order logic, such as two-variable and guarded fragments. Moreover, we also investigate the complexity of (query) conservative extensions in Horn description logics with inverse roles. Aditionally, we investigate the computational complexity of the satisfiability problem in the unary negation fragment of first-order logic extended with regular path expressions. Besides complexity results, we also study the expressive power of relation-changing modal logics. In particular, we provide translations intto hybrid logic and compare their expressive power using appropriate notions of bisimulations

Algebraic methods for hybrid logics

Ph.D. (Mathematics)Algebraic methods have been largely ignored within the eld of hybrid logics. A main theme of this thesis is to illustrate the usefulness of algebraic methods in this eld. It is a well-known fact that certain properties of a logic correspond to properties of particular classes of algebras, and that we therefore can use these classes of algebras to answer questions about the logic. The rst aim of this thesis is to identify a class of algebras corresponding to hybrid logics. In particular, we introduce hybrid algebras as algebraic semantics for the better known hybrid languages in the literature. The second aim of this thesis is to use hybrid algebras to solve logical problems in the eld of hybrid logic. Specically, we will focus on proving general completeness results for some well-known hybrid logics with respect to hybrid algebras. Next, we study Sahlqvist theory for hybrid logics. We introduce syntactically de ned classes of hybrid formulas that have rst-order frame correspondents, which are preserved under taking Dedekind MacNeille completions of atomic hybrid algebras, and which are preserved under canonical extensions of permeated hybrid algebras. Finally, we investigate the nite model property (FMP) for several hybrid logics. In particular, we give analogues of Bull's theorem for the hybrid logics under consideration in this thesis. We also show that if certain syntactically de ned classes of hybrid formulas are added to the normal modal logic S4 as axioms, we obtain hybrid logics with the nite model property

Contributions in computational intelligence with results in functional neuroimaging

This thesis applies computational intelligence methodologies to study functional brain images. It is a state-of-the-art application relative to unsupervised learning domain to functional neuroimaging. There are also contributions related to computational intelligence on topics relative to clustering validation and spatio-temporal clustering analysis. Speci_cally, there are the presentation of a new separation measure based on fuzzy sets theory to establish the validity of the fuzzy clustering outcomes and the presentation of a framework to approach the parcellation of functional neuroimages taking in account both spatial and temporal patterns. These contributions have been applied to neuroimages obtained with functional Magnetic Resonance Imaging, using both active and passive paradigm and using both in-house data and fMRI repository. The results obtained shown, globally, an improvement on the quality of the neuroimaging analysis using the methodological contributions proposed

The consistent representation of scientific knowledge : investigations into the ontology of karyotypes and mitochondria

PhD ThesisOntologies are widely used in life sciences to model scienti c knowledge. The engineering of these ontologies is well-studied and there are a variety of methodologies and techniques, some of which have been re-purposed from software engineering methodologies and techniques. However, due to the complex nature of bio-ontologies, they are not resistant to errors and mistakes. This is especially true for more expressive and/or larger ontologies. In order to improve on this issue, we explore a variety of software engineering techniques that were re-purposed in order to aid ontology engineering. This exploration is driven by the construction of two light-weight ontologies, The Mitochondrial Disease Ontology and The Karyotype Ontology. These ontologies have speci c and useful computational goals, as well as providing exemplars for our methodology. This thesis discusses the modelling decisions undertaken as well as the overall success of each ontological model. Due to the added knowledge capture steps required for the mitochondrial knowledge, The Karyotype Ontology is further developed than The Mitochondrial Disease Ontology. Speci cally, this thesis explores the use of a pattern-driven and programmatic approach to bio-medical ontology engineering. During the engineering of our biomedical ontologies, we found many of the components of each model were similar in logical and textual de nitions. This was especially true for The Karyotype Ontology. In software engineering a common technique to avoid replication is to abstract through the use of patterns. Therefore we utilised localised patterns to model these highly repetitive models. There are a variety of possible tools for the encoding of these patterns, but we found ontology development using Graphical User Interface (GUI) tools to be time-consuming due to the necessity of manual GUI interaction when the ontology needed updating. With the development of Tawny- OWL, a programmatic tool for ontology construction, we are able to overcome this issue, with the added bene t of using a single syntax to express both simple and - i - patternised parts of the ontology. Lastly, we brie y discuss how other methodologies and tools from software engineering, namely unit tests, di ng, version control and Continuous Integration (CI) were re-purposed and how they aided the engineering of our two domain ontologies. Together, this knowledge increases our understanding in ontology engineering techniques. By re-purposing software engineering methodologies, we have aided construction, quality and maintainability of two novel ontologies, and have demonstrated their applicability more generally