A new logic, sequence-indexed linear-time temporal logic (SLTL), is obtained semantically from the standard linear-time temporal logic LTL by adding a sequence modal operator which represents a sequence of symbols. By the sequence modal operator of SLTL, we can appropriately express “sequential information” in temporal reasoning. A Gentzen-type sequent calculus for SLTL is introduced, and the c...

In this paper we define a Temporal Action Theory through a combination of Answer Set Programming and Dynamic Linear Time Temporal Logic (DLTL). DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. In our language, general temporal constraints can be included in domain descriptions. We defi...

The wish to automatically construct correct systems from specifications has been around for about half a century. Church was the first one to describe this idea in 1962. Our work is closely related to this idea. We will consider systems which react to the environment denoted as open modules and our specification language is linear temporal logic (LTL). Synthesis is the problem of automatically ...

Because aerospace systems become more and more complex, the pile of documents specifying the requirements for such systems grows continuously. It is obvious that it is not enough just to produce more documents. The expressiveness of system requirements has to be considered as well. However, the ambiguity of natural language generally used to define requirements impedes a manageable growth of sy...

We propose a method for optimal Linear Temporal Logic (LTL) planning under incomplete or uncertain knowledge with a minimum required truth degree. In order to introduce modeling flexibility to the framework, we propose semantics over ranges of truth values and operators that reason over such ranges of truth values. We show that the resulting optimal planning problem can be solved efficiently. I...

In this paper we further develop the methodology of temporal logic as an executable imperative language, presented by Moszkowski [Mos86] and Gabbay [Gab87, Gab89] and present a concrete framework, called MetateM for executing (modal and) temporal logics. Our approach is illustrated by the development of an execution mechanism for a propositional temporal logic and for a restricted first order t...

We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free Büchi automata, with weights, over idempotent, zerodivisor free and totally commutative complete semirings. We show the expressive equivalence (of fragments) of these concepts, generalizing in the quantitative setup, the corresponding folklore result of formal language theory.

Proof planning is an automated reasoning technique which improves proof search by raising it to a meta-level. In this paper we apply proof planning to First-Order Linear Temporal Logic (FOLTL), which can be seen as a quantified version of Linear Temporal Logic, overcoming its finitary limitation. Automated reasoning in FOLTL is hard, since it is non-recursively enumerable; but its expressivenes...

Metric Temporal Logic (MTL) is a generalisation of Linear Temporal Logic in which the Until and Since modalities are annotated with intervals that express metric constraints. In this paper we show that over the reals MTL has the same expressive power as monadic first-order logic with binary order relation < and an infinite collection of unary functions +q, where q is a non-negative rational. Th...

We present the Temporal Logic Synthesis Format (TLSF), a high-level format to describe synthesis problems via Linear Temporal Logic (LTL). The format builds upon standard LTL, but additionally allows to use high-level constructs, such as sets and functions, to provide a compact and human-readable representation. Furthermore, the format allows to identify parameters of a specification such that ...