Tense Logic for Discrete Future Time

1970 ◽  
Vol 35 (1) ◽  
pp. 105
Author(s):  
Patrick Schindler
Keyword(s):  
Tense Logic ◽  
Future Time

Semantic analysis of tense logics

1972 ◽  
Vol 37 (1) ◽  
pp. 150-158 ◽  
Author(s):  
S. K. Thomason
Keyword(s):  
Semantic Analysis ◽  
Tense Logic ◽  
Future Time ◽  
Past Time ◽  
Substitution Instance ◽  
Image Position

Although we believe the results reported below to have direct philosophical import, we shall for the most part confine our remarks to the realm of mathematics. The reader is referred to [4] for a philosophically oriented discussion, comprehensible to mathematicians, of tense logic.The “minimal” tense logic T0 is the system having connectives ∼, →, F (“at some future time”), and P (“at some past time”); the following axioms:(where G and H abbreviate ∼F∼ and ∼P∼ respectively); and the following rules:(8) from α and α → β, infer β,(9) from α, infer any substitution instance of α,(10) from α, infer Gα,(11) from α, infer Hα.A tense logic is a system T whose language is that of T0 and whose axioms and rules include (1)–(11). The axioms and rules of T other than (1)–(11) are called proper axioms and rules.We shall investigate three systems of semantics for tense logics, i.e. three notions of structure and three relations ⊧ which stand between structures and formulas. One reads ⊧ α as “α is valid in .” A structure is a model of a tense logic T if every formula provable in T is valid in . A semantics is adequate for T if the set of models of T in the semantics is characteristic for T, i.e. if whenever T ∀ α then there is a model of T in the semantics such that ∀ α. Two structures and , possibly from different semantics, are called equivalent ( ∼ ) if exactly the same formulas are valid in as in .

Tense logic for discrete future time

1970 ◽  
Vol 35 (1) ◽  
pp. 105-118 ◽  
Author(s):  
Patrick Schindler
Keyword(s):  
Propositional Calculus ◽  
Tense Logic ◽  
Finite Model ◽  
Logical System ◽  
Model Property ◽  
Future Time ◽  
Finite Model Property ◽  
Complete Basis ◽  
Image Position ◽  
Classical Propositional Calculus

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbol G, the definitionsDf. F: Fα = NGNαDf. L: Lα = KαGα,and the postulatesis complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:Gli can be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time.

Different Future Time Perspectives Interplay in Predicting Life Satisfaction

GeroPsych ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 103-113 ◽  
Author(s):  
Minjie Lu ◽  
Angel Y. Li ◽  
Helene H. Fung ◽  
Klaus Rothermund ◽  
Frieder R. Lang
Keyword(s):  
Life Satisfaction ◽  
Time Perspective ◽  
Well Being ◽  
Future Time Perspective ◽  
Hong Kong Chinese ◽  
Future Time ◽  
Time Perspectives ◽  
Time Extension ◽  
Future Self ◽  
The Relationship

Abstract. This study addresses prior mixed findings on the relationship between future time perspective (FTP) and well-being as well as examines the associations between three aspects of FTP and life satisfaction in the health and friendship domains. 159 Germans, 97 US Americans, and 240 Hong Kong Chinese, aged 19–86 years, completed a survey on future self-views (valence) and life satisfaction. They also reported the extent to which they perceived future time as expanded vs. limited (time extension) and meaningful (openness). Findings revealed that individuals with more positive future self-views had higher satisfaction. However, those who perceived their future as more meaningful or perceived more time in their future reported higher satisfaction even when future self-views were less positive.

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