Queries and Solutions

This page documents the query object model — the Python classes that the parser builds from the ?-suffixed forms of the FDL language, what each query computes, and how to read the Solution returned by solving it. For the FDL syntax of each query see Grammatics; this page describes the runtime objects.

The query lifecycle

Every query is a subclass of Query (fuzzy_dl_owl2.fuzzydl.query.query.Query). When DLParser/DLParserFast parses an FDL file, each query form is turned into a query instance and appended to DLParser.queries_list. The typical flow is:

from fuzzy_dl_owl2.fuzzydl.parser import DLParserFast as DLParser
from fuzzy_dl_owl2.fuzzydl.milp.solution import Solution

kb, queries = DLParser.get_kb("./example.fdl")
kb.solve_kb()                       # solve the TBox once, up front

for query in queries:
    result: Solution = query.solve(kb)
    if result.is_consistent_kb():
        print(f"{query}{result}")
    print(f"Time (s): {query.get_total_time()}")

Query exposes three members used by the loop above:

• solve(kb) -> Solution — runs the query against a solved KnowledgeBase and returns a Solution.

• get_total_time() -> float — wall-clock time of the last solve, in seconds (the internal counter is nanoseconds; this accessor divides by 1e9).

• __str__() — a human-readable description of the query (used in the log output, e.g. Is audi instance of SportCar ? ).

Query classes

The table maps each FDL query keyword to the class the parser instantiates and the value the resulting Solution carries.

FDL keyword	Query class	Arguments	Result (get_solution())
sat?	KbSatisfiableQuery	—	bool — is the KB consistent
max-instance?	MaxInstanceQuery	individual, concept	float — greatest membership degree
min-instance?	MinInstanceQuery	individual, concept	float — least membership degree
all-instances?	AllInstancesQuery	concept	per-individual minimum membership
max-related?	MaxRelatedQuery	a, b, role	float — greatest relation degree
min-related?	MinRelatedQuery	a, b, role	float — least relation degree
max-subs? / min-subs?	MaxSubsumesQuery / MinSubsumesQuery (Łukasiewicz if the KB logic is Łukasiewicz, otherwise Zadeh)	concept, concept	float — subsumption degree
max-g-subs? / min-g-subs?	MaxSubsumesQuery / MinSubsumesQuery (Gödel)	concept, concept	float
max-l-subs? / min-l-subs?	MaxSubsumesQuery / MinSubsumesQuery (Łukasiewicz)	concept, concept	float
max-kd-subs? / min-kd-subs?	MaxSubsumesQuery / MinSubsumesQuery (Kleene-Dienes)	concept, concept	float
max-sat? / min-sat?	MaxSatisfiableQuery / MinSatisfiableQuery	concept, optional individual	float — best/worst satisfiability
max-var? / min-var?	MaxQuery / MinQuery	linear expression	float — optimal value of the expression
defuzzify-lom?	LomDefuzzifyQuery	concept, individual, feature	float — largest of maxima
defuzzify-mom?	MomDefuzzifyQuery	concept, individual, feature	float — middle of maxima
defuzzify-som?	SomDefuzzifyQuery	concept, individual, feature	float — smallest of maxima
bnp?	BnpQuery	fuzzy number	float — Best Non-Fuzzy Performance

Inheritance

The classes are organised by what they compute, not by max/min:

• InstanceQuery — base of MaxInstanceQuery / MinInstanceQuery (concept + individual).

• SubsumptionQuery — base of MaxSubsumesQuery / MinSubsumesQuery. The fuzzy implication variant is selected with a LogicOperatorType (LUKASIEWICZ for Łukasiewicz, GOEDEL for Gödel, KLEENE_DIENES, ZADEH), which is why a single pair of classes covers the plain, g-, l- and kd- subsumption keywords.

• SatisfiableQuery — base of MaxSatisfiableQuery / MinSatisfiableQuery; the individual argument is optional (overloaded constructor).

• RelatedQuery — base of MaxRelatedQuery / MinRelatedQuery.

• DefuzzifyQuery — base of LomDefuzzifyQuery / MomDefuzzifyQuery / SomDefuzzifyQuery (concept + individual + concrete feature name).

• MaxQuery / MinQuery — optimise a linear Expression (the max-var? / min-var? keywords) subject to KB consistency.

• KbSatisfiableQuery, AllInstancesQuery, BnpQuery derive directly from Query.

ClassificationQuery also exists in the package but is not produced by any FDL keyword; it is used internally for concept classification.

The Solution object

solve returns a fuzzy_dl_owl2.fuzzydl.milp.solution.Solution. Read it before acting on the value:

Member	Returns	Meaning
is_consistent_kb()	bool	Whether the KB was consistent. If False, the answer to any query is 1.0 and get_solution() is not meaningful.
get_solution()	bool | float	The query answer — a boolean for sat?, a float degree/value otherwise.
get_showed_variables()	dict[str, float]	Variable values requested via show-variables (and similar show-statements).
add_showed_variable(name, value)	None	Records a shown variable (used by the solver).

str(solution) is the solved value when the KB is consistent, or the literal "Inconsistent KB" otherwise. The class constants Solution.CONSISTENT_KB (True) and Solution.INCONSISTENT_KB (False) name the two consistency states.

Reading a result safely

result = query.solve(kb)
if not result.is_consistent_kb():
    # Inconsistent KB: every query trivially answers 1.0
    print("KB inconsistent")
else:
    answer = result.get_solution()      # bool for sat?, float otherwise
    print(answer)

Notes

• Solve the knowledge base once with kb.solve_kb() before iterating the queries; each query.solve(kb) then reuses the prepared KB.

• all-instances? over a KB with no individuals short-circuits — DLParserFast.main emits “There are no individuals in the fuzzy KB” instead of solving.

• For the mathematical definition of each query (the sup/inf it computes), see the Queries section of Grammatics.