ON STRONG NEIGHBOURHOOD COMPLETENESS OF MODAL AND INTERMEDIATE PROPOSITIONAL LOGICS (Part II)
نویسنده
چکیده
The property of strong neighbourhood completeness was introduced in the first part of this paper. By modifying the ultrabouqet construction, we prove this property for all Kripke-complete normal K4-logics and for a large class of Kripke-complete polymodal logics (called ‘acyclic). On the other hand, we present a simple counterexample of a polymodal logic with the f.m.p. which is not strongly neighbourhood complete.
منابع مشابه
Preservation of Admissible Rules when Combining Logics
Admissible rules are shown to be conservatively preserved by the meetcombination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of the set of admissible rules are also shown to be preserved, the latter with no penalty on the time complexity. Examples are provided for the meet-combination ...
متن کاملCombining intermediate propositional logics with classical logic
In [17], we introduced a modal logic, called L, which combines intuitionistic propositional logic IPC and classical propositional logic CPC and is complete w.r.t. an algebraic semantics. However, L seems to be too weak for Kripke-style semantics. In this paper, we add positive and negative introspection and show that the resulting logic L5 has a Kripke semantics. For intermediate logics I , we ...
متن کاملOn the relation between intuitionistic and classical modal logics
Intuitionistic propositional logic Int and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded just as fragments of classical modal logics containing S4. At the syntactical level, the Godel translation t embeds every intermediate logic L = Int+ into modal logics in the interval L = [ L = S4 t( ); L = Grz t( )]. Semantically this is re ected by ...
متن کاملFregean logics
According to Frege’s principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A ded...
متن کاملTranslation Methods for Non-Classical Logics: An Overview
This paper gives an overview on translation methods we have developed for nonclassical logics, in particular for modal logics. Optimized ’functional’ and semi-functional translation into predicate logic is described. Using normal modal logic as an intermediate logic, other logics can be translated into predicate logic as well. As an example, the translation of modal logic of graded modalities i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997