Сибирский федеральный университет

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: Asian Logic Conference; Novosibirsk, RUSSIA; Novosibirsk, RUSSIA

Год издания: 2006

Идентификатор DOI: 10.1142/9789812772749_0001

Аннотация: In Abstract Algebraic Logic, a Hilbert-style deductive system is identified with the set of its theories. This set of theories must be algebraic and must be closed under arbitrary intersections and inverse substitutions. Similarly, a Gentzen-style deductive system can be defined by providing a set of theories with similar properties, but now each theory must be a set of sequents, not just formulas. There are various kinds of Gentzen-style structures that naturally arise in connection with Hilbert systems, but in generally they fall short of being Gentzen systems. One of such structures is a family of axiomatic closure relations. Each of axiomatic closure relations is defined as a set of consequences that can be derived in the Hilbert system by modulo of some its theory, taken as the set of additional axioms. The main result of this work is the proof that a Hilbert system S admits the Deduction-Detachment Theorem if and only if the set of all axiomatic closure relations for S forms a Gentzen system.

Журнал: Mathematical Logic in Asia

Номера страниц: 1-16

Место издания: SINGAPORE

Издатель: WORLD SCIENTIFIC PUBL CO PTE LTD

• Babyonyshev Sergei V. (KRASNOYARSK STATE UNIV)

• Web of Science Core Collection