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A two‐dimensional metric temporal logic
Author(s) -
Baratella Stefano,
Masini Andrea
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201700036
Subject(s) - mathematics , axiom , sequent calculus , completeness (order theory) , sequent , discrete mathematics , gödel's completeness theorem , metric (unit) , calculus (dental) , interval temporal logic , algebra over a field , linear temporal logic , pure mathematics , algorithm , mathematical analysis , medicine , operations management , geometry , dentistry , mathematical proof , economics
We introduce a two‐dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then we prove completeness and a semantic partial cut elimination theorem down to formulas of a certain type.