A Sequent Calculus for Type Theory

Intensional models for the theory of types

Journal of Symbolic Logic ◽

10.2178/jsl/1174668386 ◽

2007 ◽

Vol 72 (1) ◽

pp. 98-118 ◽

Cited By ~ 23

Author(s):

Reinhard Muskens

Keyword(s):

Type Theory ◽

Possible Worlds ◽

Sequent Calculus ◽

Propositional Attitude ◽

Essential Elements ◽

Classical Type ◽

Logical Omniscience ◽

Small Fragment ◽

Model Existence ◽

Model Existence Theorem

AbstractIn this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up.

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Basic Simple Type Theory

10.1017/cbo9780511608865 ◽

1997 ◽

Cited By ~ 78

Author(s):

J. Roger Hindley

Keyword(s):

Type Theory ◽

Simple Type ◽

Simple Type Theory

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Type Theory and Formal Proof

10.1017/cbo9781139567725 ◽

2009 ◽

Cited By ~ 4

Author(s):

Rob Nederpelt ◽

Herman Geuvers

Keyword(s):

Type Theory ◽

Formal Proof

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Faith and Psychology: The Contribution of Empirical Research and Jungian Psychological Type Theory to Practical and Pastoral Theology

PsycEXTRA Dataset ◽

10.1037/e568892011-002 ◽

2007 ◽

Author(s):

Leslie J. Francis

Keyword(s):

Empirical Research ◽

Type Theory ◽

Pastoral Theology ◽

Psychological Type

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An empirical study in psychological type theory and biblical hermeneutics readings John 6: 5-15

PsycEXTRA Dataset ◽

10.1037/e591222013-001 ◽

2013 ◽

Author(s):

Susan H. Jones ◽

Leslie J. Francis

Keyword(s):

Empirical Study ◽

Type Theory ◽

Psychological Type ◽

Biblical Hermeneutics

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Computational Models for Multilayered Composite Shells with Application to Tires

Tire Science and Technology ◽

10.2346/1.2137509 ◽

1996 ◽

Vol 24 (1) ◽

pp. 11-38 ◽

Cited By ~ 10

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.

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Campus Social Climate Correlates of Environmental Type Dimensions

NASPA Journal ◽

10.2202/0027-6014.1397 ◽

2004 ◽

Vol 41 (4) ◽

Cited By ~ 1

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.

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