Entailment: The Logic of Relevance and Necessity

Натрийуретические пептиды (НУП) являются важными биомаркерами в диагностике и определении прогноза у пациентов с сердечной недостаточностью (СН). Оценка динамики концентрации НУП (BNP, Nt -proBNP) может быть использована в качестве критерия успешности проводимой терапии. так, при достижении целевых уровней НУП можно прогнозировать благоприятный исход заболевания. В настоящее время лечение СН с учетом уровней НУП является частью рекомендаций по лечению СН (класс IIа) и улучшению ее исхода (класс IIб) в США, однако такой подход не используется в российских клиниках. Цель. Представить современный взгляд на возможность использования НУП для оценки эффективности проводимой терапии пациентов с СН. Ключевые слова: натрийуретические пептиды, сердечная недостаточность, оценка эффективности терапии.

Федеральное государственное бюджетное учреждение «Научно-исследовательский институт комплексных проблем сердечно-сосудистых заболеваний» Сибирского отделения Российской академии медицинских наук, Кемерово, Россия

This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a ‘universal ontology’?, (ii) Is there a ‘universal formal ontology language’?, and (iii) Is there a universally applicable ‘mode of reasoning’ for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects.

Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these ...

Constructive negation, implication, and co-implication

Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification (support of truth) and the other for falsification (support of falsity). Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect to twist structures over modal algebras. Sound and complete tableau calculi are presented as well. Moreover, a number of constructive non-modal logics with strong negation are faithfully embedded into BS4, into its three-valued extension B3S4, or into temporal BS4, BtS4. These logics include David Nelson's three-valued logic N3, the four-valued logic N4 bottom, the connexive logic C, and several extensions of bi-intuitionistic logic by strong ...

Modal logics with Belnapian truth values

Reductio ad Absurdum.- Minimal Logic. Preliminary Remarks.- Logic of Classical Refutability.- The Class of Extensions of Minimal Logic.- Adequate Algebraic Semantics for Extensions of Minimal Logic.- Negatively Equivalent Logics.- Absurdity as Unary Operator.- Strong Negation.- Semantical Study of Paraconsistent Nelson's Logic.- N4?-Lattices.- The Class of N4?-Extensions.- Conclusion.

Constructive Negations and Paraconsistency

In the present article, different types of semantics for the logic N4, the paraconsistent variant of Nelson’s constructive logic with strong negation, will be considered. N4 will be characterized in terms of so-called Fidel-structures. It will be stated that Fidel-structures are equivalent to twist-structures. Further, the N4-lattices, generalization of lattices, will be defined and it will be proved that they can be represented as twist-structures. It will be proved that N4-lattices form a variety and there is a natural dual isomorphism between the lattice of subvarieties of and the lattice of N4-extensions.

Algebraic Semantics for Paraconsistent Nelson's Logic

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4-lattices are described.

Sergei P. Odintsov

Papers

Constructive Negations and Paraconsistency

Algebraic Semantics for Paraconsistent Nelson's Logic

Modal logics with Belnapian truth values

On the Representation of N4-Lattices

Inconsistency-tolerant description logic. Part II: A tableau algorithm for CALC C