Package: metric-temporal-fuzzy-logic
py-metric-temporal-fuzzy-logicWARNING: This is an experimental fork of themetric-temporal-logiclibrary,
available atmvcisback/py-metric-temporal-logic.
THis fork adds support for different fuzzy connectives to the evaluation logic; the
changes support different semantics for the core logical operations: norm (and),
conorm (or), implication, and negation (not). Unless those changes are a strong
requirement, we recommend the use of the original library.Table of ContentsAboutInstallationUsagePython Operator APIPropositional logic (using python syntax)Modal Logic (using python syntax)String based APIPropositional logic (parse api)Modal Logic (parser api)Boolean EvaluationFuzzy EvaluationQuantitative Evaluate (Signal Temporal Logic)UtilitiesSimilar ProjectsCitingAboutPython library for working with Metric Temporal Logic (MTL) with fuzzy logic. Metric
Temporal Logic is an extension of Linear Temporal Logic (LTL) for
specifying properties over time series (SeeAlur). Fuzzy Logic introduces fuzzy
valuation of the properties, as an example in the interval[0;1]as opposed to crispTrue/Falsevalues (SeeFT-LTL). The library does not introduce Fuzzy Time
operators such asalmost always. Some practical examples are given in the usage.InstallationThere is currently no release of the library. It needs to be built locally using thepoetrypython package/dependency
management tool:$ poetry buildThe package can be installed locally using your reference package manager.UsageTo begin, we importmtfl.importmtflThere aretwoAPIs for interacting with themtflmodule. Namely, one can specify the MTL expression using:Python Operators.Strings + The parse API.We begin with the Python Operator API:Python Operator APIPropositional logic (using python syntax)a,b=mtfl.parse('a'),mtfl.parse('b')phi0=~aphi1=a&bphi2=a|bphi3=a^bphi4=a.iff(b)phi5=a.implies(b)Modal Logic (using python syntax)a,b=mtfl.parse('a'),mtfl.parse('b')# Eventually `a` will hold.phi1=a.eventually()# `a & b` will always hold.phi2=(a&b).always()# `a` until `b`phi3=a.until(b)# `a` weak until `b`phi4=a.weak_until(b)# Whenever `a` holds, then `b` holds in the next two time units.phi5=(a.implies(b.eventually(lo=0,hi=2))).always()# We also support timed until.phi6=a.timed_until(b,lo=0,hi=2)# `a` holds in two time steps.phi7=a>>2String based APIPropositional logic (parse api)# - Lowercase strings denote atomic predicates.phi0=mtfl.parse('atomicpred')# - infix operators need to be surrounded by parens.phi1=mtfl.parse('((a & b & c) | d | e)')phi2=mtfl.parse('(a -> b) & (~a -> c)')phi3=mtfl.parse('(a -> b -> c)')phi4=mtfl.parse('(a <-> b <-> c)')phi5=mtfl.parse('(x ^ y ^ z)')# - Unary operators (negation)phi6=mtfl.parse('~a')phi7=mtfl.parse('~(a)')Modal Logic (parser api)# Eventually `x` will hold.phi1=mtfl.parse('F x')# `x & y` will always hold.phi2=mtfl.parse('G(x & y)')# `x` holds until `y` holds.# Note that since `U` is binary, it requires parens.phi3=mtfl.parse('(x U y)')# Weak until (`y` never has to hold).phi4=mtfl.parse('(x W y)')# Whenever `x` holds, then `y` holds in the next two time units.phi5=mtfl.parse('G(x -> F[0, 2] y)')# We also support timed until.phi6=mtfl.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.phi7=mtfl.parse('XX a')Quantitative Evaluate (Signal Temporal Logic)Given a propertyphi, one can evaluate is a timeseries satisifiesphi. Time Series can either be defined using a dictionary mapping
atomic predicate names to lists of (time,val) pairsorusing
theDiscreteSignalsAPI (used internally).There are two types of evaluation. One uses the boolean semantics of
MTL and the other uses Signal Temporal Logic like semantics.# Assumes piece wise constant interpolation.data={'a':[(0,100),(1,-1),(3,-2)],'b':[(0,20),(0.2,2),(4,-10)]}phi=mtfl.parse('F(a | b)')print(phi(data))# output: 100# Evaluate at t=3print(phi(data,time=3))# output: 2# Evaluate with discrete timephi=mtfl.parse('X b')print(phi(data,dt=0.2))# output: 2Boolean EvaluationTo Boolean semantics can be thought of as a special case of the
quantitative semantics whereTrue ↦ 1andFalse ↦ -1.  This
conversion happens automatically using thequantitative=Falseflag.# Assumes piece wise constant interpolation.data={'a':[(0,True),(1,False),(3,False)],'b':[(0,False),(0.2,True),(4,False)]}phi=mtfl.parse('F(a | b)')print(phi(data,quantitative=False))# output: Truephi=mtfl.parse('F(a | b)')print(phi(data))# output: True# Note, quantitative parameter defaults to False# Evaluate at t=3.print(phi(data,time=3,quantitative=False))# output: False# Compute sliding satisifaction.print(phi(data,time=None,quantitative=False))# output: [(0, True), (0.2, True), (4, False)]# Evaluate with discrete timephi=mtfl.parse('X b')print(phi(data,dt=0.2,quantitative=False))# output: TrueFuzzy EvaluationFuzzy evaluation considers the signals as fuzzy values or values to be
compared through fuzzy operators. The connectives used for evaluation,
that is the implementation of the basic logic operations such asandoror, can be specified through thelogicparameter. The connectives
available inmtfl.connectivearedefault,zadeh,godel,lukasiewicz, andproduct(SeeFT-LTL).a=mtfl.parse("a")b=mtfl.parse("b")d={"a":[(0,5.),(1,10.),(3,0.),(4,10.),(5,11.)],"b":[(0,15.),(2,5.),(4,10.),],}# Crisp comparison between the value of a and a constanti=a<6print(i,i(d,time=None,logic=mtfl.connective.zadeh,quantitative=True))# output: (a < 6) [(0, 1.0), (1, 0.0), (3, 1.0), (4, 0.0), (5, 0.0)]# Crisp comparison between the value of a and bi=a<bprint(i,i(d,time=None,logic=mtfl.connective.zadeh,quantitative=True))# output: (a < b) [(0, 1.0), (1, 1.0), (2, 0.0), (3, 1.0), (4, 0.0), (5, 0.0)]# Fuzzy comparison between the value of a and b, increasing as a decreases in the interval (b;b+10]i=a.lt(b,10)print(i,i(d,time=None,logic=mtfl.connective.zadeh,quantitative=True))# output: (a <[~10] b) [(0, 1.0), (1, 1.0), (2, 0.5), (3, 1.0), (4, 1.0), (5, 0.9)]# Temporal fuzzy operationi=a.lt(b,10).always()print(i,i(d,logic=mtfl.connective.zadeh,quantitative=True))# output: G(a <[~10] b) 0.5Fuzzy caveatsConsider usingquantitvative=Truewhen specifying a fuzzy logic.
Combining fuzzy and boolean evaluation might result in unexpected
behaviours due to the underlying conversion of signal values to
boolean ones.Note that the library only evaluates signals and operations at
pivot points, where their value changes. This might result in
invalid values for some connectives (product). Consider the
following example:data = {
    'a': [(0, 0.5), (1, 0.1)],
}

phi = mtfl.parse('G(a)')
print(phi(data, quantitative=False))
# output: 0.05Under theproductconnective (SeeFT-LTL), the norm operator
is defined as the product of two values.phithus evaluates to0.05 = 0.5 * 0.1across the whole signal when it should actually
tend towards0due to the repeated valuation ofa < 1at all
time instants.Utilitiesimportmtflfrommtflimportutilsprint(utils.scope(mtfl.parse('XX a'),dt=0.1))# output: 0.2print(utils.discretize(mtfl.parse('F[0, 0.2] a'),dt=0.1))# output: (a | X a | XX a)Similar ProjectsFeel free to open up a pull-request to add other similar projects. This library was written to meet some of my unique needs, for example I wanted the AST to be immutable and wanted the library tojusthandle manipulating MTL. Many other similar projects exist with different goals.https://github.com/doganulus/python-monitorshttps://github.com/STLInspector/STLInspectorCiting@misc{pyMTL,
  author       = {Marcell Vazquez-Chanlatte},
  title        = {mvcisback/py-metric-temporal-logic: v0.1.1},
  month        = jan,
  year         = 2019,
  doi          = {10.5281/zenodo.2548862},
  url          = {https://doi.org/10.5281/zenodo.2548862}
}