50,426 research outputs found
Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules
Association rules are among the most widely employed data analysis methods in
the field of Data Mining. An association rule is a form of partial implication
between two sets of binary variables. In the most common approach, association
rules are parameterized by a lower bound on their confidence, which is the
empirical conditional probability of their consequent given the antecedent,
and/or by some other parameter bounds such as "support" or deviation from
independence. We study here notions of redundancy among association rules from
a fundamental perspective. We see each transaction in a dataset as an
interpretation (or model) in the propositional logic sense, and consider
existing notions of redundancy, that is, of logical entailment, among
association rules, of the form "any dataset in which this first rule holds must
obey also that second rule, therefore the second is redundant". We discuss
several existing alternative definitions of redundancy between association
rules and provide new characterizations and relationships among them. We show
that the main alternatives we discuss correspond actually to just two variants,
which differ in the treatment of full-confidence implications. For each of
these two notions of redundancy, we provide a sound and complete deduction
calculus, and we show how to construct complete bases (that is,
axiomatizations) of absolutely minimum size in terms of the number of rules. We
explore finally an approach to redundancy with respect to several association
rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape
Principles and Implementation of Deductive Parsing
We present a system for generating parsers based directly on the metaphor of
parsing as deduction. Parsing algorithms can be represented directly as
deduction systems, and a single deduction engine can interpret such deduction
systems so as to implement the corresponding parser. The method generalizes
easily to parsers for augmented phrase structure formalisms, such as
definite-clause grammars and other logic grammar formalisms, and has been used
for rapid prototyping of parsing algorithms for a variety of formalisms
including variants of tree-adjoining grammars, categorial grammars, and
lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod
Fuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes
the ordinary inequational logic used in universal algebra. The logic deals with
atomic predicate formulas of the form of inequalities between terms and
formalizes their semantic entailment and provability in graded setting which
allows to draw partially true conclusions from partially true assumptions. We
follow the Pavelka approach and define general degrees of semantic entailment
and provability using complete residuated lattices as structures of truth
degrees. We prove the logic is Pavelka-style complete. Furthermore, we present
a logic for reasoning about graded if-then rules which is obtained as
particular case of the general result
Deduction modulo theory
This paper is a survey on Deduction modulo theor
Linear Logic for Meaning Assembly
Semantic theories of natural language associate meanings with utterances by
providing meanings for lexical items and rules for determining the meaning of
larger units given the meanings of their parts. Meanings are often assumed to
combine via function application, which works well when constituent structure
trees are used to guide semantic composition. However, we believe that the
functional structure of Lexical-Functional Grammar is best used to provide the
syntactic information necessary for constraining derivations of meaning in a
cross-linguistically uniform format. It has been difficult, however, to
reconcile this approach with the combination of meanings by function
application. In contrast to compositional approaches, we present a deductive
approach to assembling meanings, based on reasoning with constraints, which
meshes well with the unordered nature of information in the functional
structure. Our use of linear logic as a `glue' for assembling meanings allows
for a coherent treatment of the LFG requirements of completeness and coherence
as well as of modification and quantification.Comment: 19 pages, uses lingmacros.sty, fullname.sty, tree-dvips.sty,
latexsym.sty, requires the new version of Late
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