Natural Deduction Calculus for Computation Tree Logic

Abstract

We present a natural deduction calculus for the Computation Tree Logic, CTL, defined

A Labeled Natural Deduction System for a Fragment of CTL *

“…Other labeled natural deduction systems for branching time logics have been proposed, e.g. [1] and [11] both give labeled natural deduction systems for CTL. The main distinctive feature of our system is that reasoning only in terms of paths gives us the possibility of considering also the path quantifier ∀ as a modal operator and thus of getting a labeled system as clean as the ones for other modal logics [15,19].…”

Automated Natural Deduction for Propositional Linear-Time Temporal Logic

“…Following the extension of natural deduction to branching-time logic CTL [5], one of the topics for future research would be a corresponding extension of PLTL alg ND to automate the natural deduction representation of this useful logic. Another important part of our future work will be study of complexity of the method and the refinement of the searching technique with the subsequent implementation.…”

“…The ND technique initially defined for classical propositional logic was extended to first-order logic [3,4] and subsequently to the non-classical framework of propositional intuitionistic logic [13]. In [2] it was further extended to capture propositional linear-time temporal logic PLTL and in [5] the ND system was proposed for the computation tree logic CTL.…”

Approach to Formalizing UML Sequence Diagrams

“…We define the syntax of CTL in the following manner [11,12]: a set of atomic propositions AP={p, q, r, …p1, q1, r1, …p2, q2, r2, …}; classical operators: ﹁, ∧, ⇔, ∨; The distinguished feature of CTL formulae is that any temporal operator must be immediately preceded by a path quantifier. It is a basic model of CTL that temporal operators and path quantifiers are used in conjunction.…”

“…Each state contains countable atomic propositions, so the paths from one state to anther are limited. From paper [11] can be learned that the reachability of from one state to another can be solved in polynomial time when the number of states and atomic propositions is limited. So the checking for dynamic properties in sequence diagrams can be solved in polynomial time.…”