170 research outputs found
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 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
Uncovering Probabilistic Implications in Typological Knowledge Bases
The study of linguistic typology is rooted in the implications we find
between linguistic features, such as the fact that languages with object-verb
word ordering tend to have post-positions. Uncovering such implications
typically amounts to time-consuming manual processing by trained and
experienced linguists, which potentially leaves key linguistic universals
unexplored. In this paper, we present a computational model which successfully
identifies known universals, including Greenberg universals, but also uncovers
new ones, worthy of further linguistic investigation. Our approach outperforms
baselines previously used for this problem, as well as a strong baseline from
knowledge base population.Comment: To appear in Proceedings of ACL 201
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 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. By exploiting a previously noted alternative view of this entailment in terms of linear programming duality, we characterize exactly the cases of entailment from arbitrary numbers of premises. 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.Peer ReviewedPostprint (author's final draft
Approximate reasoning using terminological models
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved
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