Syllogistic Logic with “Most”

Endrullis, Jörg; Moss, Lawrence S.

doi:10.1007/978-3-662-47709-0_10

Cited by 22 publications

(16 citation statements)

References 4 publications

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“…For complete proof-theoretic semantics of most wrt same and all in syllogistic logic seeEndrullis and Moss (2015). Similar rules that account for additional semantics of few and many are presented in Section 5 as they coincide with efficient rules for other quantifiers.…”

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confidence: 79%

Natural Solution to FraCaS Entailment Problems

Abzianidze

2016

Proceedings of the Fifth Joint Conference on Lexical and Computational Semantics

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Reasoning over several premises is not a common feature of RTE systems as it usually requires deep semantic analysis. On the other hand, FraCaS is a collection of entailment problems consisting of multiple premises and covering semantically challenging phenomena. We employ the tableau theorem prover for natural language to solve the FraCaS problems in a natural way. The expressiveness of a type theory, the transparency of natural logic and the schematic nature of tableau inference rules make it easy to model challenging semantic phenomena. The efficiency of theorem proving also becomes challenging when reasoning over several premises. After adapting to the dataset, the prover demonstrates state-of-the-art competence over certain sections of FraCaS.

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confidence: 79%

Natural Solution to FraCaS Entailment Problems

Abzianidze

2016

Proceedings of the Fifth Joint Conference on Lexical and Computational Semantics

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“…This paper can be thought of as a continuation of the latter work. It is also related to recent studies of Moss [4], Endrullis and Moss [2], and a recent work of Moss and Topal [5].…”

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confidence: 82%

Most-Intersection of Countable Sets

Çevik¹,

Topal²

2020

Preprint

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We introduce a novel set-intersection operator called 'most-intersection' based on the logical quantifier 'most, via natural density of countable sets, to be used in determining the majority characteristic of a given countable infinite collection of systems. The new operator determines based on the natural density, the elements which are in 'most' sets in a given infinite collection. This notion allows one to define a majority set-membership characteristic of an infinite collection with minimal information loss, compared to the standard intersection operator, when used in statistical ensembles. We also give some applications of the most-intersection operator in formal language theory. The introduction of the most-intersection operator leads to a large number of applications in pure and applied mathematics.

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“…Endrullis and Moss [32] introduced a syllogistic logic containing the quantifier most on finite sets. They provided the semantics of the sentence Most A are B in a given model as follows:…”

Section: "Most" and Its Historical Surroundingsmentioning

confidence: 99%

Natural Density and the Quantifier “Most”

Topal

Çevik

2020

J of Log Lang and Inf

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This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form "Most A are B ", where A and B are plural nouns and the interpretations of A and B are infinite subsets of N. There are two widely used semantics for Most A are B : (i) C(A ∩ B) > C(A \ B) and (ii) C(A ∩ B) > C(A) 2 , where C(X) denotes the cardinality of a Mathematics Subject Classification (2010). 03B65, 03C80, 11B05.

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Syllogistic Logic with “Most”

Cited by 22 publications

References 4 publications

Natural Solution to FraCaS Entailment Problems

Natural Solution to FraCaS Entailment Problems

Most-Intersection of Countable Sets

Natural Density and the Quantifier “Most”

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