Automated Natural Deduction for Propositional Linear-Time Temporal Logic

Abstract

We present a proof searching technique for the natural deduction calculus for the propositional linear-time temporal logic and prove its correctness. This opens the prospect to apply our technique as an automated reasoning tool in a number of emerging computer science applications and in a deliberative decision making framework across various AI applications.

Labelled Tableaux for Distributed Temporal Logic

“…, where V(A) is the set of variables V i and of label terms headed by a Skolem function occurring in A; 4 At this point, labels whose head is a Skolem function symbol are treated as if they were simply variables.…”

“…However, it is interesting to note that our system for local reasoning seems to be closely related to the natural deduction system for future-time LTL of [4], which was developed in parallel with our work. We have begun investigating whether similar rules would also be suited for the extension to global reasoning in both past-time and future-time DTL and plan to report on this soon.…”

“…If one really wants to hard-wire loop checking in our system, then exploring different rules, for instance those of [4], may be interesting. It may be possible here to capitalize on the constraint graphs we used in our tableaux system.…”

A Labeled Tableaux System for the Distributed Temporal Logic DTL

“…Rules for the logical connectives and the temporal operators. We illustrate the use of the tableaux system with an ex- 2 Note that the trichotomy rule may lead to considerable branching in the tableaux. In [1], we have replaced this rule by a set of rules that permit only controlled forms of trichotomy.…”

“…We have designed our systems with the aim of providing tableaux for full DTL, including past, but it is interesting to note that our system for local reasoning seems to be closely related to the natural deduction system for futuretime LTL of [2], which was developed in parallel with our work. We have begun investigating whether the rules of [2] would also be suited for the extension to global reasoning in past and future-time DTL, and plan to report on this soon.…”