### Abstract

We introduce a theory of temporal logic operators using sets of natural numbers as time domain, formalized in a shallow embedding manner. The theory comprises special natural intervals (theory IL_Interval: open and closed intervals, continuous and modulo intervals, interval traversing results), operators for shifting intervals to left/right on the number axis as well as expanding/contracting intervals by constant factors (theory IL_IntervalOperators.thy), and ultimately definitions and results for unary and binary temporal operators on arbitrary natural sets (theory IL_TemporalOperators).

### License

BSD License

### Topics

- Logic/General logic/Temporal logic

### Session Nat-Interval-Logic

- IL_Interval
- IL_IntervalOperators
- IL_TemporalOperators

### Depends on

- Infinite Lists

### Used by

- AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics

## Cite

×

Nat-Interval-Logic-AFP

    @article{Nat-Interval-Logic-AFP,
      author  = {David Trachtenherz},
      title   = {Interval Temporal Logic on Natural Numbers},
      journal = {Archive of Formal Proofs},
      month   = {February},
      year    = {2011},
      note    = {\url{https://isa-afp.org/entries/Nat-Interval-Logic.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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