An Expressively Complete Temporal Logic without Past Tense Operators for Mazurkiewicz Traces

1999 ◽  
pp. 188-203 ◽  
Author(s):  
Volker Diekert ◽  
Paul Gastin
Keyword(s):  
Temporal Logic ◽  
Past Tense ◽  
Tense Operators ◽  
Mazurkiewicz Traces

The Selectional Restrictions of French Past Tenses

2002 ◽  
Vol 47 (1-2) ◽  
pp. 47-66
Author(s):  
Marie Labelle
Keyword(s):  
Past Tense ◽  
External Argument ◽  
Internal Argument ◽  
Selectional Restrictions ◽  
Tense Operators ◽  
Past Tenses

AbstractThis article argues against the idea that the Imparfait and the Passé Simple in French are aspectually sensitive tense operators. Both morphemes combine with any type of eventuality. It is not the case that a clause in the Imparfait denotes a state, or that a clause in the Passé Simple denotes an event. It is proposed that the Passé Simple is a true past tense, which introduces a past eventuality in the discourse with the condition that it be the maximal eventuality of the appropriate type. The Imparfait is analyzed as a dyadic morpheme, which selects an eventuality as internal argument and a past temporal referent of discourse as external argument, where the eventuality provides a condition on the temporal referent.

Effect algebras with a full set of states

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Ivan Chajda
Keyword(s):  
Temporal Logic ◽  
Effect Algebra ◽  
Effect Algebras ◽  
Tense Operators ◽  
Numerical Algebra ◽  
Full Set Of States

AbstractIt is shown that every effect algebra with a full set of states can be represented as a so-called numerical algebra introduced in the paper. For numerical algebras there are introduced tense operators which indicate dynamical changes of quantum events depending on variability of states. These operators enable to recognize an effect algebra with a full set of states as a temporal logic where events are quantified by these tense operators. The problem of representation of tense operators on a given numerical algebra is solved.

Tense and temporal logic

2018 ◽  
Author(s):  
Quentin Smith
Keyword(s):  
Temporal Logic ◽  
Special Kind ◽  
Tense Logic ◽  
Abstract Objects ◽  
Ontological Commitments ◽  
Tense Operators ◽  
Sentential Logic ◽  
Present Tense ◽  
Tensed Theory

A special kind of logic is needed to represent the valid kinds of arguments involving tensed sentences. The first significant presentation of a tense logic appeared in Prior (1957). Sentential tense logic, in its simplest form, adds to classical sentential logic two tense operators, P and F. The basic idea is to analyse past and future tenses in terms of prefixes ‘It was true that’ and ‘It will be true that’, attached to present-tensed sentences. (Present-tensed sentences do not need present tense operators, since ‘It is true that Jane is walking’ is equivalent to ‘Jane is walking’.) Translating the symbols into English is merely a preliminary to a semantics for tense logic; we may translate ‘P’ as ‘it was true that’ but we still have the question of the meaning of ‘it was true that’. There are at least two versions of the tensed theory of time – the minimalist version and the maximalist version – that can be used for the interpretation of the tense logic symbols. The minimalist version implies that there are no past or future particulars, and thus no things or events that have properties of pastness or futurity. What exists are the things, with their properties and relations, that can be mentioned in certain present-tensed sentences. If ‘Jane is walking’ is true, then there is a thing, Jane, which possesses the property of walking. ‘Socrates was discoursing’, even if true, does not contain a name that refers to a past thing, Socrates, since there are no past things. The ontological commitments of past and future tensed sentences are merely to propositions, which are sentence-like abstract objects that are the meanings or senses of sentences. ‘Socrates was discoursing’ merely commits us to the proposition expressed by the sentence ‘It was true that Socrates is discoursing’. The maximalist tensed theory of time, by contrast, implies that there are past, present and future things and events; that past items possess the property of pastness, present items possess the property of presentness, and future items possess the property of being future. ‘Socrates was discoursing’ involves a reference to a past thing, Socrates, and implies that the event of Socrates discoursing has the property of being past.

scholarly journals An Expressive Extension of TLC

1999 ◽  
Vol 6 (26) ◽  
Author(s):  
Jesper G. Henriksen
Keyword(s):  
Distributed Systems ◽  
Temporal Logic ◽  
Linear Time ◽  
Expressive Power ◽  
Dependence Relation ◽  
Linear Time Temporal Logic ◽  
Causal Chains ◽  
Mazurkiewicz Traces ◽  
Do So

A temporal logic of causality (TLC) was introduced by Alur, Penczek<br />and Peled in [1]. It is basically a linear time temporal logic<br />interpreted over Mazurkiewicz traces which allows quantification over<br />causal chains. Through this device one can directly formulate causality<br />properties of distributed systems. In this paper we consider an<br />extension of TLC by strengthening the chain quantification operators.<br />We show that our logic TLC  adds to the expressive power of TLC.<br />We do so by defining an Ehrenfeucht-Fraissé game to capture the expressive<br /> power of TLC. We then exhibit a property and by means of<br />this game prove that the chosen property is not definable in TLC. We<br />then show that the same property is definable in TLC. We prove in<br />fact the stronger result that TLC is expressively stronger than TLC<br />exactly when the dependence relation associated with the underlying<br />trace alphabet is not transitive.

scholarly journals An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces

1996 ◽  
Vol 3 (62) ◽  
Author(s):  
P. S. Thiagarajan ◽  
Igor Walukiewicz
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Order Reduction ◽  
Expressive Power ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Reduction Methods ◽  
Linear Time Temporal Logic ◽  
Mazurkiewicz Traces

<p>A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications.</p><p>We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also provides a syntactic characterisation of the so-called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.</p>

AN EXPRESSIVE EXTENSION OF TLC

2002 ◽  
Vol 13 (03) ◽  
pp. 341-360 ◽  
Author(s):  
JESPER GULMANN HENRIKSEN
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Expressive Power ◽  
Order Logic ◽  
Dependency Relation ◽  
Linear Time Temporal Logic ◽  
Causal Chains ◽  
Second Order Logic ◽  
Monadic Second Order Logic ◽  
Mazurkiewicz Traces

A temporal logic of causality (TLC) was introduced by Alur, Penczek, and Peled in [1]. It is basically a linear time temporal logic interpreted over Mazurkiewicz traces which allows quantification over causal chains. Through this device one can directly formulate causality properties of distributed systems. In this paper we consider an extension of TLC by strengthening the chain quantification operators. We show that our logic TLC* adds to the expressive power of TLC. We doso by defining an Ehrenfeucht-Fraïssé game to capture the expressive power of TLC. We then exhibit a property and by means of this game prove that the chosen property is not definable in TLC. We then show that the same property is definable in TLC*. We prove in fact the stronger result that TLC* is expressively stronger than TLC exactly when the dependency relation associated with the underlying trace alphabet is not transitive. We then show that TLC* defines only regular trace languages by embedding it into the monadic second-order logic. Finally, the relative expressive power of TLC* and similar logics for traces is compared.

Zero Marking of Past Tense in Child African American English

2014 ◽  
Vol 21 (4) ◽  
pp. 173-181 ◽  
Author(s):  
Ryan Lee ◽  
Janna B. Oetting
Keyword(s):  
African American ◽  
American English ◽  
African American English ◽  
Current Paper ◽  
Past Tense ◽  
Typically Developing ◽  
Grammatical Function

Zero marking of the simple past is often listed as a common feature of child African American English (AAE). In the current paper, we review the literature and present new data to help clinicians better understand zero marking of the simple past in child AAE. Specifically, we provide information to support the following statements: (a) By six years of age, the simple past is infrequently zero marked by typically developing AAE-speaking children; (b) There are important differences between the simple past and participle morphemes that affect AAE-speaking children's marking options; and (c) In addition to a verb's grammatical function, its phonetic properties help determine whether an AAE-speaking child will produce a zero marked form.

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