We prove that the Buchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of the space of infinite labelled binary trees;in particular the Buchi and the Muller...
详细信息
We prove that the Buchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of the space of infinite labelled binary trees;in particular the Buchi and the Muller topologies are not Polish in this case.
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as d-logics. Unlike logics based on the topological closure operator, d-logics have not p...
详细信息
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as d-logics. Unlike logics based on the topological closure operator, d-logics have not previously been studied in the framework of dynamical systems, which are pairs (X, f) consisting of a topological space X equipped with a continuous function f : X -> X. We introduce the logics wK4C, K4C and GLC and show that they all have the finite Kripke model property and are sound and complete with respect to the d-semantics in this dynamical setting. In particular, we prove that wK4C is the d-logic of all dynamic topological systems, K4C is the d-logic of all TD dynamic topological systems, and GLC is the d-logic of all dynamic topological systems based on a scattered space. We also prove a general result for the case where f is a homeomorphism, which in particular yields soundness and completeness for the corresponding systems wK4H, K4H and GLH. The main contribution of this work is the foundation of a general proof method for finite model property and completeness of dynamic topological d-logics. Furthermore, our result for GLC constitutes the first step towards a proof of completeness for the trimodal topo-temp oral language with respect to a finite axiomatisation - something known to be impossible over the class of all spaces.
We consider logics which define different properties of functions - such as injectivity, surjectivity, monotonicity, etc. - in the context of temporalxmodal logic. In this type of logics, the possible worlds semantics...
详细信息
We consider logics which define different properties of functions - such as injectivity, surjectivity, monotonicity, etc. - in the context of temporalxmodal logic. In this type of logics, the possible worlds semantics is modified by considering each world as a temporal flow and using accessibility functions to represent the connection among them. This approach is adequate to model interactions between processes with clocks that can be either synchronized or not. We study the definability and give indexed axiomatic systems for these properties.
In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the...
详细信息
In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, Euclidean and serial properties of relations in the context of a functional approach for temporalmodal logic. The main result is the proof of definability of these definitions which is obtained by using algebraic characterizations. As a consequence, we will have in our temporalmodal context the generalizations of modal logics T, S4, S5, KD45, etc. These new logics will allow us to establish connections among time flows in very different ways, which enables us to carry out different relations among asynchronous systems. Our further research is focused on the construction of logics with these properties and the design of theorem provers for these logics.
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-ci...
详细信息
暂无评论