A Hierarchy of Temporal Logics with Past

We extend the classical hierarchy of branching-time temporal logics between UB and CTL* by studying which additional expressive power (if any) stems from the incorporation of past-time modalities. In addition, we propose a new temporal combinator, N for “Now”, that brings new and interesting expressive power. In several situations, non-trivial translation algorithms exist from a temporal logic with past to a pure-future fragment. These algorithms have important practical applications e.g. in the field of model-checking.

[1]  Joseph Y. Halpern,et al.  Decision procedures and expressiveness in the temporal logic of branching time , 1982, STOC '82.

[2]  Edward Y. Chang,et al.  Characterization of Temporal Property Classes , 1992, ICALP.

[3]  Edmund M. Clarke,et al.  Characterizing Finite Kripke Structures in Propositional Temporal Logic , 1988, Theor. Comput. Sci..

[4]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[5]  Moshe Y. Vardi A temporal fixpoint calculus , 1988, POPL '88.

[6]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[7]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[8]  Wolfgang Thomas,et al.  Computation Tree Logic CTL* and Path Quantifiers in the Monadic Theory of the Binary Tree , 1987, ICALP.

[9]  Zohar Manna,et al.  A Decision Algorithm for Full Propositional Temporal Logic , 1993, CAV.

[10]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[11]  Philippe Schnoebelen,et al.  Translation Results for Modal Logics of Reactive Systems , 1993, AMAST.

[12]  Inmaculada Perez de Guzmán,et al.  A new algebraic semantic approach and some adequate connectives for computation with temporal logic over discrete time , 1992, J. Appl. Non Class. Logics.

[13]  Louise E. Moser,et al.  Completeness and Soundness of Axiomatizations for Temporal Logics. Without Next , 1994, Fundam. Informaticae.

[14]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[15]  Mordechai Ben-Ari,et al.  The temporal logic of branching time , 1981, POPL '81.

[16]  Dov M. Gabbay,et al.  The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems , 1987, Temporal Logic in Specification.

[17]  Saharon Shelah,et al.  On the temporal analysis of fairness , 1980, POPL '80.

[18]  Alberto Zanardo,et al.  Ockhamist Computational Logic: Past-Sensitive Necessitation in CTL , 1993, J. Log. Comput..

[19]  Colin Stirling,et al.  Modal and temporal logics , 1993, LICS 1993.

[20]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[21]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[22]  Edmund M. Clarke,et al.  Characterizing Correctness Properties of Parallel Programs Using Fixpoints , 1980, ICALP.

[23]  E. Clarke,et al.  Automatic Veriication of Nite-state Concurrent Systems Using Temporal-logic Speciications. Acm , 1993 .

[24]  Zohar Manna,et al.  The anchored version of the temporal framework , 1988, REX Workshop.

[25]  François Laroussinie Logique temporelle avec passé pour la spécification et la vérification des systèmes réactifs , 1994 .

[26]  Grzegorz Rozenberg,et al.  Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency , 1988, Lecture Notes in Computer Science.