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Bulletin of the Section of Logic, 2023 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 ...
Emma van Dijk +2 more
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Multimodal Dependent Type Theory [PDF]
Logical Methods in Computer Science, 2021 We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode theory allow us
Daniel Gratzer +3 more
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Normalisation by Evaluation for Type Theory, in Type Theory [PDF]
Logical Methods in Computer Science, 2017 We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types.
Thorsten Altenkirch, Ambrus Kaposi
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Dualized Simple Type Theory [PDF]
Logical Methods in Computer Science, 2017 We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus.
Harley Eades III +2 more
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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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