2,855 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
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
Relevance and Conditionals: A Synopsis of Open Pragmatic and Semantic Issues
Recently several papers have reported relevance effects on the cognitive assessments of indicative conditionals, which pose an explanatory challenge to the Suppositional Theory of conditionals advanced by David Over, which is influential in the psychology of reasoning. Some of these results concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this chapter is to take a Birdseye view on the debate and investigate some of the open theoretical issues posed by the empirical results. Central among these is whether to count these effects as belonging to pragmatics or semantics
Justifying Inference to the Best Explanation as a Practical Meta-Syllogism on Dialectical Structures
This article discusses how inference to the best explanation (IBE) can be justified as a practical meta-argument. It is, firstly, justified as a *practical* argument insofar as accepting the best explanation as true can be shown to further a specific aim. And because this aim is a discursive one which proponents can rationally pursue in--and relative to--a complex controversy, namely maximising the robustness of one's position, IBE can be conceived, secondly, as a *meta*-argument. My analysis thus bears a certain analogy to Sellars' well-known justification of inductive reasoning (Sellars 1969); it is based on recently developed theories of complex argumentation (Betz 2010, 2011)
Revamping Hypothetico-Deductivism: A Dialectic Account of Confirmation
We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2011). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of novelty
On the Role of Canonicity in Bottom-up Knowledge Compilation
We consider the problem of bottom-up compilation of knowledge bases, which is
usually predicated on the existence of a polytime function for combining
compilations using Boolean operators (usually called an Apply function). While
such a polytime Apply function is known to exist for certain languages (e.g.,
OBDDs) and not exist for others (e.g., DNNF), its existence for certain
languages remains unknown. Among the latter is the recently introduced language
of Sentential Decision Diagrams (SDDs), for which a polytime Apply function
exists for unreduced SDDs, but remains unknown for reduced ones (i.e. canonical
SDDs). We resolve this open question in this paper and consider some of its
theoretical and practical implications. Some of the findings we report question
the common wisdom on the relationship between bottom-up compilation, language
canonicity and the complexity of the Apply function
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