Relative Entailment Among Probabilistic Implications

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probabilit...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Logical methods in computer science Ročník 15, Issue 1
Hlavní autoři: Atserias, Albert, Balcázar, José L., Piceno, Marie Ely
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Logical Methods in Computer Science e.V 06.02.2019
Témata:
Algorísmica i teoria de la complexitat
Aprenentatge automàtic
Computer logic
computer science - databases
computer science - logic in computer science
computer science - machine learning
Informàtica
Informàtica teòrica
Knowledge representation (Information theory)
Logic in Computer Science
Lògica informàtica
Machine learning
Representació del coneixement (Teoria de la informació)
Àrees temàtiques de la UPC
ISSN:1860-5974, 1860-5974
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probability of the consequent, given the antecedent: we are dealing with what the data analysis community calls confidence of partial implications or association rules. Existing studies of redundancy among these partial implications have characterized so far only entailment from one premise and entailment from two premises, both in the stand-alone case and in the case of presence of additional classical implications (this is what we call "relative entailment"). By exploiting a previously noted alternative view of the entailment in terms of linear programming duality, we characterize exactly the cases of entailment from arbitrary numbers of premises, again both in the stand-alone case and in the case of presence of additional classical implications. As a result, we obtain decision algorithms of better complexity; additionally, for each potential case of entailment, we identify a critical confidence threshold and show that it is, actually, intrinsic to each set of premises and antecedent of the conclusion.
ISSN:1860-5974
1860-5974
DOI:10.23638/LMCS-15(1:10)2019