Logics For Qualitative Reasoning

Veloso, Paulo A. S.; Carnielli, Walter

doi:10.1007/978-1-4020-2808-3_23

Cited by 7 publications

(21 citation statements)

References 17 publications

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“…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: 98%

“…These extensions are proper, because some sentences, such as ∃u∇zu z, cannot be expressed without ∇. (See, e. g., [17] and [14]. )…”

Section: Axiomatics Of Ultrafilter Logicmentioning

confidence: 99%

“…Then, voracious animals are generic for general voracity and non-flying animals are generic with respect to generally not flying (see, e. g., [17]). …”

Section: Generic Elements and Functionsmentioning

confidence: 99%

“…(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%

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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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Section: Ultrafilter Logicmentioning

confidence: 98%

“…These extensions are proper, because some sentences, such as ∃u∇zu z, cannot be expressed without ∇. (See, e. g., [17] and [14]. )…”

Section: Axiomatics Of Ultrafilter Logicmentioning

confidence: 99%

“…Then, voracious animals are generic for general voracity and non-flying animals are generic with respect to generally not flying (see, e. g., [17]). …”

Section: Generic Elements and Functionsmentioning

confidence: 99%

“…(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%

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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.…”

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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Methodical Construction of Symbolic Diagrams

Veloso

2008

Lecture Notes in Computer Science

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Logics For Qualitative Reasoning

Cited by 7 publications

References 17 publications

On Ultrafilter Logic and Special Functions

On Ultrafilter Logic and Special Functions

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

Methodical Construction of Symbolic Diagrams

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