A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B)

2004 ◽  
Keyword(s):  
Type Theory ◽  
Proper Extension

scholarly journals Predicate Logic with Anaphora

1994 ◽  
Vol 4 ◽  
pp. 79 ◽  
Author(s):  
Paul Dekker
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Discourse Representation ◽  
Dynamic Predicate Logic ◽  
Proper Extension ◽  
Update Semantics ◽  
Anaphoric Pronouns ◽  
Separate Treatment

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

Predicate Logic with Anaphora

2015 ◽  
pp. 79
Author(s):  
Paul Dekker
Keyword(s):  
Type Theory ◽  
Predicate Logic ◽  
Discourse Representation ◽  
Dynamic Predicate Logic ◽  
Proper Extension ◽  
Update Semantics ◽  
Anaphoric Pronouns ◽  
Separate Treatment

In this paper I make a case for a separate treatment of (singular) anaphoric pronouns within a predicate logic with anaphora (PLA). Discourse representation theoretic results (from Kamp 1981) can be formulated in a compositional way, without fid­dling with orthodox notions of scope and binding. In contrast with its predecessor dynamic predicate logic (Groenendijk and Stokhof 1991), the system of PLA is a proper extension of ordinary predicate logic and it has a genuine update semantics. Moreover, in contrast with other compositional reformulations of DRT, the seman­tics of PLA remains well within the bounds of ordinary, extensional type theory.

scholarly journals Observational equality: now for good

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-27
Author(s):  
Loïc Pujet ◽  
Nicolas Tabareau
Keyword(s):  
Type Theory ◽  
Identity Relation ◽  
Logical Relation ◽  
Type Checking ◽  
Dependent Type Theory ◽  
Proper Extension ◽  
New Type ◽  
Recent Extension ◽  
Dependent Type

Building on the recent extension of dependent type theory with a universe of definitionally proof-irrelevant types, we introduce TTobs, a new type theory based on the setoidal interpretation of dependent type theory. TTobs equips every type with an identity relation that satisfies function extensionality, propositional extensionality, and definitional uniqueness of identity proofs (UIP). Compared to other existing proposals to enrich dependent type theory with these principles, our theory features a notion of reduction that is normalizing and provides an algorithmic canonicity result, which we formally prove in Agda using the logical relation framework of Abel et al. Our paper thoroughly develops the meta-theoretical properties of TTobs, such as the decidability of the conversion and of the type checking, as well as consistency. We also explain how to extend our theory with quotient types, and we introduce a setoidal version of Swan's Id types that turn it into a proper extension of MLTT with inductive equality.

Type Theory and Formal Proof

2009 ◽  
Author(s):  
Rob Nederpelt ◽  
Herman Geuvers
Keyword(s):  
Type Theory ◽  
Formal Proof

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

Campus Social Climate Correlates of Environmental Type Dimensions

NASPA Journal ◽  
2004 ◽  
Vol 41 (4) ◽  
Author(s):  
Daniel W. Salter ◽  
Reynol Junco ◽  
Summer D. Irvin
Keyword(s):  
Work Environment ◽  
Personal Growth ◽  
Type Theory ◽  
General Purpose ◽  
Myers Briggs Type Indicator ◽  
Environment Scale ◽  
Type Indicator ◽  
Group Environment ◽  
System Maintenance ◽  
Environment Type

To address the ability of the Salter Environment Type Assessment (SETA) to measure different kinds of campus environments, data from three studies of the SETA with the Work Environment Scale, Group Environment Scale, and University Residence Environment Scale were reexamined (n = 534). Relationship dimension scales were very consistent with extraversion and feeling from environmental type theory. System maintenance and systems change scales were associated with judging and perception on the SETA, respectively. Results from the SETA and personal growth dimension scales were mixed. Based on this analysis, the SETA may serve as a general purpose environmental assessment for use with the Myers-Briggs Type Indicator.

Coq plugin for the Reasonably Exceptional Type Theory

2019 ◽  
Author(s):  
Pierre-Marie P�drot ◽  
Nicolas Tabareau ◽  
Hans Jacob Fehrmann ◽  
�ric Tanter
Keyword(s):  
Type Theory
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