Infinitely many precomplete with respect to parametric expressibility classes of formulas in a provability logic of propositions
نویسنده
چکیده
In the present paper we consider a non-tabular extension L of the well-known propositional provability logic GL together with the notion of parametric expressibility of formulas in a logic proposed by A. V. Kuznetsov. We prove that there are infinitely many precomplete with respect to parametric expressibility classes of formulas in the above mentioned logic L.
منابع مشابه
On parametrical expressibility in the free void-generated diagonalizable algebra
Let A be any universal algebra. We say formula A is explicitly expressible on algebra A via system of formulas Σ, if A can be obtained on A of variables and formulas of Σ by means of superpositions. We say a system of formulas Σ is complete in A, if any formula is expressible via Σ. We say a system Σ is precomplete as to expressibility on A if Σ is not complete on A, but for any formula F , whi...
متن کاملOn sufficient conditions for expressibility of constants in the 4-valued extension of the propositional provability logic $GL$
In the present paper we consider the simplest non-classical extension GL4 of the well-known propositional provability logic GL together with the notion of expressibility of formulas in a logic proposed by A. V. Kuznetsov. Conditions for expressibility of constants in GL4 are found out, which were first announced in a author’s paper in 1996.
متن کاملOn a syntactic approximation to logics that capture complexity classes
We formulate a formal syntax of approximate formulas for the logic with counting quantifiers, SOLP, studied by us in [1], where we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P andNL; (ii) weakening the ordering relation to an almost order (in the sense of [7]) we can separate meani...
متن کاملFinite Proofs for Infinitary Formulas
Recent work has shown that the infinitary logic of hereand-there is closely related to the input language of the ASP grounder gringo. A formal system axiomatizing that logic exists, but a proof in that system may include infinitely many formulas. In this note, we define a correspondence between the validity of infinitary formulas in the logic of here-and-there and the provability of formulas in...
متن کاملProving infinitary formulas
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic exists, but a proof in that system may include infinitely many formulas. In this note we describe a relationship between the validity of infinitary formulas in ...
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 2014