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An Automated Theorem Prover (ATP) for Interval Temporal Logic (ITL) has always been a
desirable tool. There have been various attempts to implement such ATPs:
- Lite. Shinji Kono (1991 (Prolog), 2008 (Java)).
Tableau-based, exponential in the number of the variables in the formula and
also combinatorial w.r.t. to the nesting of temporal logic operators.
- ITL Library for PVS. Antonio Cau (1997).
Interactive theorem prover for (in)finite first order ITL, requires expert proof
knowledge and has little automation.
- DCVALID. Paritosh Pandya (2000).
Quantified Discrete time Duration Calculus (QDDC). Translate QDDC into
WS1S, use decision procedure of WS1S (MONA, Nils Klarlund and Anders
Møller). WS1S has non-elementary complexity.
- PITL2Mona. Rodolfo Gomez (2004).
Translate finite Propositional ITL (PITL) into WS1S, use decision procedure of
WS1S (MONA). WS1S has non-elementary complexity.
- FL2CUDD. Ben Moszkowski (2005).
Use a subset of (in)finite PITL called Fusion Logic (FL). The decision procedure
of FL is built on top of Colorado University Decision Diagram (CUDD, Fabio
So mainly modelchecking or special purpose automated deduction. [2mm] There are
off-the-shelf automated proof and counterexample search tools (ATP) for first-order and
Inspired by the work of Peter Höffner, Georg Struth and Bernhard Möller we proceed as
- Introduce Interval Temporal Algebra (ITA). An ITA is based on Kleene Algebra
and Omega Algebra.
- Show that PITL is an ITA.
- Encode the axiom system for ITA in an off-the shelf ATP Prover9 (first-order
and equational logic, William McCune).