Ultrafilter logic and generic reasoning

Carnielli, Walter; Veloso, Paulo A. S.

doi:10.1007/3-540-63385-5_31

Cited by 15 publications

(15 citation statements)

References 8 publications

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“…(We are considering a universe of birds. If there are other animals, we use sorts: the birds form a subsort of the universe; see e. g. [4] and [17]. )…”

Section: Logics For 'Generally'mentioning

confidence: 99%

“…In this section we briefly review ultrafilter logic: its syntax, semantics and axiomatics (cf. also [4], [17] and [16]). We consider a fixed denumerably infinite set V of symbols for variables.…”

Section: Ultrafilter Logicmentioning

confidence: 99%

“…The development will concentrate on the ultrafilter logic in [4] and [16], but its main lines can be appropriately adapted to some other logics for 'generally'; for instance, filter logic (for 'most') and upward closed logic (for 'several'). Ultrafilter logic can be regarded as an extreme case of these logics with interesting properties.…”

Section: Introductionmentioning

confidence: 99%

“…). 7 Hence, we have monotonicity and substitutivity of equivalents, as well as prenex forms: each formula is equivalent to a prefix of quantifiers followed by a quantifier-free matrix (cf [4]. and[16]).…”

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confidence: 99%

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On Ultrafilter Logic and Special Functions

Veloso

2004

Stud Logica

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Logics for 'generally' were introduced for handling assertions with vague notions, such as 'generally', 'most', 'several', etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.

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“…(We are considering a universe of birds. If there are other animals, we use sorts: the birds form a subsort of the universe; see e. g. [4] and [17]. )…”

Section: Logics For 'Generally'mentioning

confidence: 99%

Section: Ultrafilter Logicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On Ultrafilter Logic and Special Functions

Veloso

2004

Stud Logica

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“…For example in linguistics and natural language [29,5], artificial intelligence [30,17,24,14], and philosophy [33] similar logical notions were developed. Another example is ultrafilter logic [12,34] capturing the intuition of 'most' by means of generalised quantifiers over ultrafilters. In [32], a condensed survey of generalized quantifiers in applied logic, linguistics and computer science is presented.…”

Section: Introductionmentioning

confidence: 99%

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

Cruz-Filipe¹,

Rasga²,

Sernadas³

et al. 2008

Journal of Logic and Computation

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Following recent developments in the topic of generalized quantifiers, and also having in mind applications in the areas of security and artificial intelligence, a conservative enrichment of (two-sorted) first-order logic with almost-everywhere quantification is proposed. The completeness of the axiomatization against the measure-theoretic semantics is carried out using a variant of the LindenbaumHenkin technique. The independence of the axioms is analyzed, and the almosteverywhere quantifier is compared with related notions of generalized quantification. A suitable fragment of the logic is translated to first-order logic and validity is shown to be preserved.

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On Special Functions and Theorem Proving in Logics for ‘Generally’

Veloso¹,

Veloso²

2002

Advances in Artificial Intelligence

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Ultrafilter logic and generic reasoning

Cited by 15 publications

References 8 publications

On Ultrafilter Logic and Special Functions

On Ultrafilter Logic and Special Functions

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

On Special Functions and Theorem Proving in Logics for ‘Generally’

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