Results 11 to 20 of about 6,236,903 (286)
Manuscrito, 2023 It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types.
Bruno Bentzen
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AGAINST CUMULATIVE TYPE THEORY [PDF]
The Review of Symbolic Logic, 2021 AbstractStandard Type Theory, ${\textrm {STT}}$ , tells us that $b^n(a^m)$ is well-formed iff $n=m+1$ . However, Linnebo and Rayo [23] have advocated the use of Cumulative Type Theory, $\textrm {CTT}$ , which has more relaxed type-restrictions: according to $\textrm {CTT}$ , $b^\beta (a^\alpha )$ is well-formed iff $\beta>\alpha $ . In this
Trueman, Rob, Button, Tim
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Type Theory with Opposite Types: A Paraconsistent Type Theory
Logic Journal of the IGPL, 2021 Abstract A version of intuitionistic type theory is extended with opposite types, allowing a different formalization of negation and obtaining a paraconsistent type theory ($\textsf{PTT} $). The rules for opposite types in $\textsf{PTT} $ are based on the rules of the so-called constructible falsity.
Juan C Agudelo-Agudelo +1 more
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Semantics for Combinatory Logic With Intersection Types
Frontiers in Computer Science, 2022 There is a plethora of semantics of computational models, nevertheless, the semantics of combinatory logic are among the less investigated ones. In this paper, we propose semantics for the computational system of combinatory logic with intersection types.
Silvia Ghilezan +2 more
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Dynamic Semiosis: Meaning, Informing, and Conforming in Constructing the Past
Information, 2023 Constructed Past Theory (CPT) is an abstract representation of how information about the past is produced and interpreted. It is grounded in the assertion that whatever we can write or say about anything in the past is the product of cognition ...
Kenneth Thibodeau
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Type theory in type theory using quotient inductive types [PDF]
ACM SIGPLAN Notices, 2016 We present an internal formalisation of a type heory with dependent types in Type Theory using a special case of higher inductive types from Homotopy Type Theory which we call quotient inductive types (QITs). Our formalisation of type theory avoids referring to preterms or a typability relation but defines directly well typed objects by an inductive ...
Altenkirch, Thorsten, Kaposi, Ambrus
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Call-by-name Gradual Type Theory [PDF]
Logical Methods in Computer Science, 2020 We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments
Max S. New, Daniel R. Licata
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Al-Lisaniyyat, 2022 The aim of our paper is to present the Constructive Type Theory (CTT) and some related concepts for the Swedish logician Per Martin Löf, who constructed a formal logic system in order to establish a philosophical foundation of constructive mathematics ...
Terkia Mechouet, Farid Zidani
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2-adjoint equivalences in homotopy type theory [PDF]
Logical Methods in Computer Science, 2021 We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
Daniel Carranza +3 more
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Multi-level Contextual Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification, characterize ...
Mathieu Boespflug, Brigitte Pientka
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