Existential Generalization in TIL

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F17%3A10235979" target="_blank" >RIV/61989100:27240/17:10235979 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/47813059:19240/17:A0000111

Výsledek na webu

<a href="http://dx.doi.org/10.5593/sgem2017/21/S07.040" target="_blank" >http://dx.doi.org/10.5593/sgem2017/21/S07.040</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5593/sgem2017/21/S07.040" target="_blank" >10.5593/sgem2017/21/S07.040</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existential Generalization in TIL

Popis výsledku v původním jazyce

The paper deals with the fundamental rule of extensional logics, namely the rule of Existential Generalization. This rule can be applied in the situation when a function f is applied on its argument a to obtain the value of f at a. If the application does not fail, i.e., if the function f is defined at a, then we can existentially quantify, and derive that there is the value f(a). Our system is based on Transparent Intensional Logic (TIL). Since TIL is a hyperintensional, partial, typed lambda calculus, we examine the validity of the rule in TIL, or rather in its computational variant the TIL-Script language. The rule is context sensitive in the sense that depending on a context we should recognize the type of entity to be abstracted over. This is not to say that the rule can be invalid dependently on context; the rule is valid universally. Only that the type of the argument over which we quantity depends on the context. There are three kinds of contexts to be distinguished, namely extensional, intensional and hyperintensonal. We introduce the definition of these three kinds of context and an algorithm that recognizes in which context a particular construction occurs so that the Existential Generalization can be validly applied. The tool navigates users through the correct application of the deduction rules.

Název v anglickém jazyce

Existential Generalization in TIL

Popis výsledku anglicky

The paper deals with the fundamental rule of extensional logics, namely the rule of Existential Generalization. This rule can be applied in the situation when a function f is applied on its argument a to obtain the value of f at a. If the application does not fail, i.e., if the function f is defined at a, then we can existentially quantify, and derive that there is the value f(a). Our system is based on Transparent Intensional Logic (TIL). Since TIL is a hyperintensional, partial, typed lambda calculus, we examine the validity of the rule in TIL, or rather in its computational variant the TIL-Script language. The rule is context sensitive in the sense that depending on a context we should recognize the type of entity to be abstracted over. This is not to say that the rule can be invalid dependently on context; the rule is valid universally. Only that the type of the argument over which we quantity depends on the context. There are three kinds of contexts to be distinguished, namely extensional, intensional and hyperintensonal. We introduce the definition of these three kinds of context and an algorithm that recognizes in which context a particular construction occurs so that the Existential Generalization can be validly applied. The tool navigates users through the correct application of the deduction rules.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA15-13277S" target="_blank" >GA15-13277S: Hyperintensionální logika pro analýzu přirozeného jazyka</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

17th International Multidisciplinary Scientific GeoConference: SGEM 2017 : conference proceedings : 29 June-5 July, 2017, Albena, Bulgaria. Volume 17. Issue 21

ISBN

978-619-7408-01-0

ISSN

1314-2704

e-ISSN

neuvedeno

Počet stran výsledku

8

Strana od-do

311-318

Název nakladatele

STEF92 Technology Ltd.

Místo vydání

Sofia

Místo konání akce

Albena

Datum konání akce

29. 6. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—