First-order queries over temporal databases inexpressible in temporal logic

1996 ◽  
pp. 305-324 ◽  
Author(s):  
David Toman ◽  
Damian Niwiński
Keyword(s):  
Temporal Logic ◽  
Temporal Databases ◽  
First Order

Towards the Temporal Approach to Abstract Data Types

1988 ◽  
Vol 11 (1) ◽  
pp. 49-63
Author(s):  
Andrzej Szalas
Keyword(s):  
Temporal Logic ◽  
Abstract Data Types ◽  
Data Types ◽  
First Order ◽  
Abstract Data ◽  
Order Completeness ◽  
General Method

In this paper we deal with a well known problem of specifying abstract data types. Up to now there were many approaches to this problem. We follow the axiomatic style of specifying abstract data types (cf. e.g. [1, 2, 6, 8, 9, 10]). We apply, however, the first-order temporal logic. We introduce a notion of first-order completeness of axiomatic specifications and show a general method for obtaining first-order complete axiomatizations. Some examples illustrate the method.

scholarly journals Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (8) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Dynamic Logic ◽  
Order Theory ◽  
Simple Extension ◽  
Propositional Dynamic Logic ◽  
First Order ◽  
Time Semantics ◽  
Linear Time Temporal Logic ◽  
Obvious Manner

A simple extension of the propositional temporal logic of linear<br />time is proposed. The extension consists of strengthening the until<br />operator by indexing it with the regular programs of propositional<br />dynamic logic (PDL). It is shown that DLTL, the resulting logic, is<br />expressively equivalent to S1S, the monadic second-order theory<br />of omega-sequences. In fact a sublogic of DLTL which corresponds<br />to propositional dynamic logic with a linear time semantics is<br />already as expressive as S1S. We pin down in an obvious manner<br />the sublogic of DLTL which correponds to the first order fragment<br />of S1S. We show that DLTL has an exponential time decision<br />procedure. We also obtain an axiomatization of DLTL. Finally,<br />we point to some natural extensions of the approach presented<br />here for bringing together propositional dynamic and temporal<br />logics in a linear time setting.

FINITE STATE PROCESSES, Z-TEMPORAL LOGIC AND THE MONADIC THEORY OF THE INTEGERS

1992 ◽  
Vol 03 (03) ◽  
pp. 233-244 ◽  
Author(s):  
A. SAOUDI ◽  
D.E. MULLER ◽  
P.E. SCHUPP
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Second Order ◽  
Regular Languages ◽  
Infinite Words ◽  
First Order ◽  
Monadic Theory ◽  
Finite State ◽  
Temporal Formula

We introduce four classes of Z-regular grammars for generating bi-infinite words (i.e. Z-words) and prove that they generate exactly Z-regular languages. We extend the second order monadic theory of one successor to the set of the integers (i.e. Z) and give some characterizations of this theory in terms of Z-regular grammars and Z-regular languages. We prove that this theory is decidable and equivalent to the weak theory. We also extend the linear temporal logic to Z-temporal logic and then prove that each Z-temporal formula is equivalent to a first order monadic formula. We prove that the correctness problem for finite state processes is decidable.

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