论文信息 - Axiomatisation and decidability ofF andP in cyclical time

Axiomatisation and decidability ofF andP in cyclical time

We present a Hilert style axiomatisation for the set of formulas in the temporal language withF andP which are valid over non-transitive cyclical flows of time.We also give a simpler axiomatisation using the slightly controversial ‘irreflexivity rule’ and go on to prove the decidability of any temporal logic over cyclical time provided it uses only connectives with first-order tables.

Mark Reynolds | Mark Reynolds

[1] Dov M. Gabbay,et al. An Axiomitization of the Temporal Logic with Until and Since over the Real Numbers , 1990, J. Log. Comput..

[2] Ian M. Hodkinson,et al. Completeness , 2020, Mathematics of the Bond Market: A Lévy Processes Approach.

[3] Mark Reynolds,et al. An axiomatization for until and since over the reals without the IRR rule , 1992, Stud Logica.

[4] A. H. Lachlan,et al. Countable homogeneous tournaments , 1984 .

[5] John P. Burgess,et al. Basic Tense Logic , 1984 .

[6] Leon Henkin,et al. The completeness of the first-order functional calculus , 1949, Journal of Symbolic Logic.

[7] Peter J. Cameron. Oligomorphic Permutation Groups: Subgroups , 1990 .

[8] D. Gabbay. Expressive Functional Completeness in Tense Logic (Preliminary report) , 1981 .

[9] Jaakko Hintikka,et al. Time And Modality , 1958 .

[10] Yde Venema. Completeness via Completeness , 1993 .

[11] M. Rabin. Decidability of second-order theories and automata on infinite trees , 1968 .

[12] W. H. Newton-Smith,et al. The Structure of Time , 2018 .

[13] E. V. Huntington,et al. A new set of postulates for betweenness, with proof of complete independence , 1924 .

[14] D. Gabbay,et al. Temporal expressive completeness in the presence of gaps , 1993 .

[15] Johan van Benthem,et al. The Logic of Time , 1983 .