Inductive Logic Programming

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Formulas S entails formula F iff...
all models of S also make F true
a clause
a conjunction (?) of literals
a definite clause
a clause with exactly one non-negated atom: h :- b,b,b.
atom
predicate and terms p(a,b, ...)
term
constant, variable or functor
literal
atom or negated atom
substitution
a mapping from variables to constants
grounding substitution of atom a
a substitution that maps all variables of a to constants
fact
a clause without body (may contain variables !)
program
a set of clauses
background theory or program
a set of background facts
sequential covering algorithm
learn one rule, remove the data it covers, repeat
refinement operator
operator that creates candidate atoms to add to a clause
marginalisation
computing the probability (the marginal) of random variables given some evidence p(a | e)
most probable explanation (MPE)
most likely joint state of the random variables given the evidence
weighted model counting
"counting the number of satisfying model, according to their probability", for marginalisation
weighted max-sat
"maximizing the satisfaction criteria"
weighted boolean formula
"the possible proofs derived from a program"
learning from interpretation
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learning from entailment
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theory in conjunctive normal form (CNF)
a conjunction of disjunctions of literals, i.e. of clauses
propositional logic
a logic where terms are either constants or functors (but not variables)
Herbrand base of a FOL first-order logic theory
all possible ground atoms constructed with the predicates, functors and constants
Herbrand interpretation, or (possible) world
assignment of a truth value to all (ground) atoms in the Herbrand base (consistent with the theory or not)
model of a theory
an Herbrand interpretation (or world) consistent with the theory (all formulas/clauses are true)
conjunction
a formula with AND
disjunction
a formula with OR
normal clause, or rule
universally quantified expression of the form h :- b,b,b.
normal program
a set of normal clauses
definite program
negation-free logic program
LHM Least Herbrand Model of a logic program
the smallest of all Herbrand Models. It contains all ground atoms entailed by the logic program (and no undefined ones)
well-founded semantics
a semantic where atoms can be true, false or undefined ("bottom")
closed world assumption
everything that is not implied to be true is assumed to be false
intensional probabilistic fact
probabilistic clause used to define the domains of the variables of a predicate
probabilistic atom
an atom that unifies with a ground probabilistic fact (opposite: derived atom)
derived atom
an atom that unifies with the head of some rule (opposite: probabilistic atom)
range-restricted clause
all variables in the head should appear in a positive literal in the body
atomic choice
"the choice to include (or not) a ground probabilistic fact (in a possible world)"
total choice
any subset of the set of all ground probabilistic fact
Example of Least Herbrand Model
FOL theory {a ← b} has 3 models {¬a,¬b}, {a,¬b},{a, b}.
LP {a :- b} has only one model {¬a,¬b}
ProbLog program
ground probalistic fact + intensional probabilistic facts + logic program (for derived atoms)
well-formed formula
all variables in the formula are quantified
A set of formulas S is inconsistent iff...
A set of formulas S has no model
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