Existential generalization in TIL

@inproceedings{29780,
   author = {Menšík, Marek and Kermaschek, Jakub and Cienciala, Luděk},
   address = {Sofia},
   booktitle = {International Multidisciplinary Scientific GeoConference Surveying Geology and Mining Ecology Management, SGEM},
   doi = {http://dx.doi.org/10.5593/sgem2017/21/S07.040},
   edition = {Volume 17},
   keywords = {Deduction; Existential Generalization; Extension; Hyperintension; Intension; Logic; TIL},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Sofia},
   isbn = {978-619-7408-01-0},
   pages = {311-318},
   publisher = {International Multidisciplinary Scientific Geoconference},
   title = {Existential generalization in TIL},
   year = {2017}
}

TY  - JOUR
ID  - 29780
AU  - Menšík, Marek - Kermaschek, Jakub - Cienciala, Luděk
PY  - 2017
TI  - Existential generalization in TIL
PB  - International Multidisciplinary Scientific Geoconference
CY  - Sofia
SN  - 9786197408010
KW  - Deduction
KW  - Existential Generalization
KW  - Extension
KW  - Hyperintension
KW  - Intension
KW  - Logic
KW  - TIL
N2  - 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.
ER  - 

MENŠÍK, Marek, Jakub KERMASCHEK a Luděk CIENCIALA. Existential generalization in TIL. Online. In \textit{International Multidisciplinary Scientific GeoConference Surveying Geology and Mining Ecology Management, SGEM}. Volume 17. Sofia: International Multidisciplinary Scientific Geoconference, 2017. s.~311-318. ISBN~978-619-7408-01-0. Dostupné z: https://dx.doi.org/10.5593/sgem2017/21/S07.040. [citováno 2024-04-24]