Rasiowa–Sikorski deduction systems in computer science applications

AbstractA Rasiowa-Sikorski system is a sequence-type formalization of logics. The system uses invertible decomposition rules which decompose a formula into sequences of simpler formulae whose validity is equivalent to validity of the original formula. There may also be expansion rules which close indecomposable sequences under certain properties of relations appearing in the formulae, like symmetry or transitivity. Proofs are finite decomposition trees with leaves having “fundamental”, valid labels. The author describes a general method of applying the R-S formalism to develop complete deduction systems for various brands of C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specification logic with McCarthy's connectives and Kleene quantifiers, a logic for nondeterministic specifications, many-sorted FOL with possibly empty carriers of some sorts, and a three-valued logic for reasoning about concurrency

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure

Foundations of Rule-Based Query Answering

This survey article introduces into the essential concepts and methods underlying rule-based query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundation-oriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the “Rule Interchange Framework (RIF)” currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in F-Logic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed

Aplicación de algebras fork en la verificación automática de sistemas especificados en lógica modal

En este trabajo los sistemas de software son especificados por medio de un grafo y las propiedades que debe cumplir son expresadas como fórmulas de la lógica modal KPI. Ambos, sistema y propiedades, son traducidos a relaciones de un álgebra Fork. Con estas relaciones resultantes se puede alimentar al sistema RELVIEW, el cual permite verificar automáticamente si dichas propiedades se verifican en el sistema diseñado.Eje: TeoríaRed de Universidades con Carreras en Informática (RedUNCI

Aplicación de algebras fork en la verificación automática de sistemas especificados en lógica modal

En este trabajo los sistemas de software son especificados por medio de un grafo y las propiedades que debe cumplir son expresadas como fórmulas de la lógica modal KPI. Ambos, sistema y propiedades, son traducidos a relaciones de un álgebra Fork. Con estas relaciones resultantes se puede alimentar al sistema RELVIEW, el cual permite verificar automáticamente si dichas propiedades se verifican en el sistema diseñado.Eje: TeoríaRed de Universidades con Carreras en Informática (RedUNCI

Categorical Ontology I - Existence

The present paper is the first piece of a series whose aim is to develop an approach to ontology and metaontology through category theory. We exploit the theory of elementary toposes to claim that a satisfying ``theory of existence'', and more at large ontology itself, can both be obtained through category theory. In this perspective, an ontology is a mathematical object: it is a category, the universe of discourse in which our mathematics (intended at large, as a theory of knowledge) can be deployed. The internal language that all categories possess prescribes the modes of existence for the objects of a fixed ontology/category. This approach resembles, but is more general than, fuzzy logics, as most choices of \clE and thus of \Omega_\clE yield nonclassical, many-valued logics. Framed this way, ontology suddenly becomes more mathematical: a solid corpus of techniques can be used to backup philosophical intuition with a useful, modular language, suitable for a practical foundation. As both a test-bench for our theory, and a literary divertissement, we propose a possible category-theoretic solution of Borges' famous paradoxes of Tlön's ``nine copper coins'', and of other seemingly paradoxical construction in his literary work. We then delve into the topic with some vistas on our future works