Temat: type theory - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Core Type Theory
Autorzy:: van Dijk, Emma
Ripley, David
Gutierrez, Julian
Tematy:: core logic
type theory
strong normalization; Pokaż więcej
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Powiązania:: https://bibliotekanauki.pl/articles/43181538.pdf Link otwiera się w nowym oknie
Opis:: Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 2.

Tytuł:: Identity, equality, nameability and completeness. Part II
Autorzy:: Manzano, María
Moreno, Manuel Crescencio
Tematy:: identity
equality
completeness
nameability
first-order modal logic
hybrid logic
hybrid type theory
equational hybrid propositional type theory; Pokaż więcej
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Powiązania:: https://bibliotekanauki.pl/articles/749980.pdf Link otwiera się w nowym oknie
Opis:: This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity is a notion used to define other logical concepts. In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic with standard semantics a reliable definition of identity is possible. In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using the nominals and the @ operator. We finish our paper in the kingdom of identity where the only primitives are lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation. We have found at the end of our walk a possible point of convergence in the logic Equational Hybrid Propositional Type Theory (EHPTT), [14] and [15].
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 3.

Tytuł:: An outline of type-theoretical approaches to lexical semantics
Autorzy:: Cooper, R.
Retoré, C.
Tematy:: lexical semantics
compositional semantics
type theory
lambda calculus; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Podstaw Informatyki PAN
Powiązania:: https://bibliotekanauki.pl/articles/103831.pdf Link otwiera się w nowym oknie
Opis:: We take the opportunity of the publication of some of the papers of the ESSLLI workshop TYTLES (TYpe Theory and LExical Semantics, ESSLLI 2015, Barcelona) to provide an overview of the possibilities that type theory offers to model lexical semantics, especially the type-theoretical frameworks that properly model compositional semantics.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 4.

Tytuł:: Interfacing language, spatial perception and cognition in Type Theory with Records
Autorzy:: Dobnik, S.
Cooper, R.
Tematy:: spatial language
TTR
Type Theory with Records
computational framework; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Podstaw Informatyki PAN
Powiązania:: https://bibliotekanauki.pl/articles/103889.pdf Link otwiera się w nowym oknie
Opis:: We argue that computational modelling of perception, action, language, and cognition introduces several requirements of a formal semantic theory and its practical implementations in situated dialogue agents. Using examples of semantic representations of spatial descriptions we show how Type Theory with Records (TTR) satisfies these requirements and provides a promising knowledge representation system for situated agents.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 5.

Tytuł:: Isomorphisms in EQ-Algebras
Autorzy:: Bakhshi, M.
Khavari, M.R.
Nazifi, M.
Tematy:: many-valued logics
Fuzzy type theory
EQ-algebra
homomorphism theorems; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795508.pdf Link otwiera się w nowym oknie
Opis:: In this paper we investigate some isomorphism theorems in EQ-algebras. After establishing some basic results we give the Fundamental Homomorphism Theorem and by using it we state and prove some other isomorphism theorems. We also state and prove a correspondence theorem. Next, using some results of the theory of universal algebra we characterize subdirectly irreducible EQ-algebras.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 6.

Tytuł:: Type Theories and Lexical Networks : using Serious Games as the basis for Multi-Sorted Typed Systems
Autorzy:: Chatzikyriakidis, S.
Lafourcade, M.
Ramadier, L.
Zarrouk, M.
Tematy:: lexical networks
JeuxDeMots
type theory
type ontologies
formal semantics
natural language inference; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Podstaw Informatyki PAN
Powiązania:: https://bibliotekanauki.pl/articles/103833.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we show how a rich lexico-semantic network which Has been built using serious games, JeuxDeMots, can help us in grounding our semantic ontologies in doing formal semantics using rich or modern type theories (type theories within the tradition of Martin Löf). We discuss the issue of base types, adjectival and verbal types, hyperonymy/hyponymy relations as well as more advanced issues like homophony and polysemy. We show how one can take advantage of this wealth of lexical semantics in a formal compositional semantics framework. We argue that this is a way to sidestep the problem of deciding what the type ontology should look like once a move to a many sorted type system has been made. Furthermore, we show how this kind of information can be extracted from a lexico-semantic Network like JeuxDeMots and inserted into a proof-assistant like Coq in order to perform reasoning tasks.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 7.

Tytuł:: A categorical model of predicate linear logic
Autorzy:: Demeterová, E.
Mihályi, D.
Novitzká, V.
Tematy:: linear type theory
predicate linear logic
symmetric monoidal closed category; Pokaż więcej
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Powiązania:: https://bibliotekanauki.pl/articles/122570.pdf Link otwiera się w nowym oknie
Opis:: Linear logic is one of the logical systems with special properties suitable for describing real processes used in computer science. It enables one to specify dynamics, non determinism, consecutive processes and important resources as memory and time on syntactic level. Moreover, its deduction system enables one to verify specified properties. Constructing an appropriate model based on categories can serve for modeling various program systems in the wide spectrum of computer science. Mainly, propositional linear logic is used for these purposes. The expression power of linear logic significantly grows by extending propositional logic with predicates and quantifiers. Our paper concerns itself with defining predicate linear logic together with its deduction system and our main aim is to construct a categorical model of predicate linear logic as a symmetric monoidal closed category.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 8.

Tytuł:: Identity, Equality, Nameability and Completeness
Autorzy:: Manzano, María
Moreno, Manuel Crescencio
Tematy:: first-order logic
type theory
identity
equality
indiscernibility
comprehension
completeness
translations
nameability; Pokaż więcej
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Powiązania:: https://bibliotekanauki.pl/articles/750030.pdf Link otwiera się w nowym oknie
Opis:: This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first case, one investigates what kind of logic is required. In the second case, one is interested in the definition of the other logical concepts (connectives and quantifiers) in terms of the identity relation, using also abstraction. The present paper investigates whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic a reliable definition of identity is possible. However, the definition needs the standard semantics and we know that with this semantics completeness is lost. We have also studied the relationship of equality with comprehension and extensionality and pointed out the relevant role played by these two axioms in Henkin’s completeness method. We finish our paper with a section devoted to general semantics, where the role played by the nameable hierarchy of types is the key in Henkin’s completeness method.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 9.

Tytuł:: Quantification in Programming Languages.
Kwantyfikacja w Językach Programowania
Autorzy:: Gaiński, Piotr
Opis:: Kwantyfikacja jest ważnym pojęciem w teorii typów, które zaimplementowane jest w wielu nowoczesnych językach programowania. Wprowadza ona dwa istotne mechanizmy: polimorfizm parametryczny oraz abstrakcję danych. Wiążę się również z dwoma kluczowymi właściwościami systemów typów: ekspresyjnością oraz rozstrzygalnością problemu sprawdzania typu. W niniejszej pracy przedstawię teoretyczne podstawy kwantyfikacji opartej na rachunku lambda, opiszę kilka podstawowych systemów typów, które zawierają kwantyfikację oraz omówię kwantyfikację w kontekście trzech nowoczesnych języków programowania: Javy, Scali oraz języka C#.
Quantification is an important concept in type theory and is employed in numerous modern programming languages. It introduces two vital mechanisms: parametric polymorphism and data abstraction. It is closely related to crucial theoretical properties of type systems: expressiveness and decidability of type-checking. In this paper I am going to briefly introduce theoretical foundations of quantification based on the lambda calculus, describe some basic type systems, which incorporate quantification, and finally discuss quantification in the context of three modern programming languages: Java, Scala and C#.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

Inne

na półce

Skocz do pozycji: 10.

Tytuł:: Asymptotic densities in logic and type theory
Autorzy:: Zaionc, Marek
Kostrzycka, Zofia
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

Artykuł

na półce

Informacja

Wyszukujesz frazę "type theory" wg kryterium: Temat