Products of ‘ transitive ’ modal logics . Part I : ‘ negative ’ results Draft
نویسندگان
چکیده
Here we solve a number of major open problems concerning computational properties of products and commutators of two ‘transitive’ (but not ‘symmetric’) standard modal logics (such as, e.g., K4, S4, S4.1, Grz, or GL) by showing that all of them are undecidable and lack the (abstract) finite model property. Some of these products turn out to be even not recursively enumerable and some commutators Kripke incomplete.
منابع مشابه
Products of ‘transitive’ modal logics without the (abstract) finite model property
It is well known that many two-dimensional products of modal logics with at least one ‘transitive’ (but not ‘symmetric’) component lack the product finite model property. Here we show that products of two ‘transitive’ logics (such as, e.g., K4 ×K4, S4 × S4, Grz×Grz and GL×GL) do not have the (abstract) finite model property either. These are the first known examples of 2D modal product logics w...
متن کاملOn PSPACE-decidability in Transitive Modal Logics
In this paper we describe a new method, allowing us to prove PSPACE-decidability for transitive modal logics. We apply it to L1 and L2, modal logics of Minkowski spacetime. We also show how to extend this method to some other transitive logics.
متن کاملA Resolution-Based Decision Procedure for Extensions of K4
This paper presents a resolution decision procedure for transitive propositional modal logics. The procedure combines the relational translation method with an ordered chaining calculus designed to avoid unnecessary inferences with transitive relations. We show the logics K4, KD4 and S4 can be transformed into a bounded class of well-structured clauses closed under ordered resolution and negati...
متن کاملNon-primitive recursive decidability of products of modal logics with expanding domains
We show that—unlike products of ‘transitive’ modal logics which are usually undecidable— their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite...
متن کاملSimulation of Two Dimensions in Unimodal Logics
In this paper, we prove undecidability and the lack of finite model property for a certain class of unimodal logics. To do this, we adapt the technique from [7], where products of transitive modal logics were investigated, for the unimodal case. As a particular corollary, we present an undecidable unimodal fragment of Halpern and Shoham’s Interval Temporal Logic.
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 2004