Tense Operators on BL-algebras and its Applications

In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.

Tense operators on frameable equality algebras

Abstract: In this paper, we introduce the frameable equality algebras and use the concept of tense operators on them to define tense equality algebras. We investigate some algebraic properties of tense equality algebras and prove the representation theory for strict strong tense equality algebras. Then we introduce the notions of (prime) tense deductive systems and tense congruences and obtain some structural theorems.

Tense De Morgan S4-algebras

In [Tense operators on De Morgan algebras, Log. J. IGPL 22(2) (2014) 255–267], Figallo and Pelaitay introduced the notion of tense operators on De Morgan algebras. Also, other notions of tense operators on De Morgan algebras were given by Chajda and Paseka in [De Morgan algebras with tense operators, J. Mult.-Valued Logic Soft Comput. 1 (2017) 29–45; The Poset-based logics for the De Morgan negation and set representation of partial dynamic De Morgan algebras, J. Mult.-Valued Logic Soft Comput. 31(3) (2018) 213–237; Set representation of partial dynamic De Morgan algebras, in 2016 IEEE 46th Int. Symp. Multiple-Valued Logic (IEEE Computer Society, 2016), pp. 119–124]. In this paper, we introduce a new notion of tense operators on De Morgan algebras and define the class of tense De Morgan [Formula: see text]-algebras. The main purpose of this paper is to give a discrete duality for tense De Morgan [Formula: see text]-algebras. To do this, we will extend the discrete duality given in [W. Dzik, E. Orłowska and C. van Alten, Relational Representation Theorems for Lattices with Negations: A Survey, Lecture Notes in Computer Science (2006), pp. 245–266], for De Morgan algebras.

Advanced Temporalizing

There is a widespread assumption that B-theorists—according to whom there is no fundamental distinction between present and non-present times—should interpret tense operators such as ‘It was the case that’ and ‘It will be the case five minutes hence that’ as implicit quantifier-restrictors, so that (for example) an utterance at the present time n of the sentence ‘It was the case that there are dinosaurs’ is true just in case there are dinosaurs located at some time t earlier than n. However, it is easy to show that this interpretation of the tense operators causes problems for B-theorists when combined with certain other natural B-theoretic commitments. In this paper, I argue that a good way for B-theorists to avoid these problems is to treat the tense operators as redundant when the sentences in their scope are qualitative—that is, not about any particular individual(s).

Tense and Interperspectival Content

Is tense, as some contend, merely a feature of language (linguistic tense) or is it used to express some perspectival feature of the world? Many have argued that a proper analysis of linguistic tense would say that the tense operators in natural language express nonperspectival features of the world—that past and future linguistic tense are just used to express static universal relations between events or times. Tensers and detensers are split on precisely this point: tensers take tense to express an irreducible and real perspectival feature of the world, and detensers think it is a superficial property of language or thought that refers to aperspectival contents. In this chapter tense is among several examples of perspectival content. It is argued that perspectival contents, or interperspectival contents, are expressed in different ways from different perspectival positions.

Tense and temporal logic

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.

Vrijeme i determiniza

Does the definition of modality with the tense operators point to the thesis of universal determinism? Is the theorem about predetermination provable within the framework of tense logic and is with this the above-mentioned thesis proved also?Diodorus Kronos's main conclusion can be interpreted as an attempt to give an affirmative answer to the first question. Both analyses offered in this article show, however, that the determinism is presupposed in the premises of thia conclusion.The answer to the second question is somewhat more complex. This is discussed in the second part of the article.