[](https://travis-ci.org/mvcisback/py-metric-temporal-logic) [](https://codecov.io/gh/mvcisback/py-metric-temporal-logic) # About Python library for working with Metric Temporal Logic (MTL). Metric Temporal Logic is an extension of Linear Temporal Logic (LTL) for specifying properties over time series (See [Alur][1]). Some practical examples are given in the usage. # Installation `$ pip install metric-temporal-logic` # Usage To begin, we import `mtl`. ```python import mtl ``` ## Propositional logic (using parse api) ```python # - Lowercase strings denote atomic predicates. phi0 = mtl.parse('atomicpred') # - Binary operators need to be surrounded by parens. phi1 = mtl.parse('((a & b & c) | d | e)') phi2 = mtl.parse('(a -> b) & (~a -> c)') phi3 = mtl.parse('(a -> b -> c)') phi4 = mtl.parse('(a <-> b <-> c)') phi5 = mtl.parse('(x ^ y ^ z)') # - Unary operators (negation) phi6 = mtl.parse('~a') phi7 = mtl.parse('~(a)') ``` ## Propositional logic (using python syntax) ```python a, b = mtl.parse('a'), mtl.parse('b') phi0 = ~a phi1 = a & b phi2 = a | b # TODO: add phi3 = a ^ b phi4 = a.iff(b) phi5 = a.implies(b) ``` ## Modal Logic (parser api) ```python # Eventually `x` will hold. phi1 = mtl.parse('F x') # `x & y` will always hold. phi2 = mtl.parse('G(x & y)') # `x` holds until `y` holds. # Note that since `U` is binary, it requires parens. phi3 = mtl.parse('(x U y)') # Whenever `x` holds, then `y` holds in the next two time units. phi4 = mtl.parse('G(x -> F[0, 2] y)') # We also support timed until. phi5 = mtl.parse('(a U[0, 2] b)') # Finally, if time is discretized, we also support the next operator. # Thus, LTL can also be modeled. # `a` holds in two time steps. phi6 = mtl.parse('XX a') ``` [1]: https://link.springer.com/chapter/10.1007/BFb0031988