In this paper we look at the suitability of modern interval-based temporal logic for modeling John Buridan’s treatment of tensed sentences in his Sophismata. Building on the paper, we develop Buridan’s analysis of temporal logic, paying particular attention to his notions of negation and the absolute/relative nature of the future and the past.We introduce a number of standard modern propositional interval temporal logics to illustrate where Buridan’s interval-based temporal analysis differs from the standard modern approaches. We give formal proofs of (...) some claims in, and sketch how the standard modern systems could be defined in terms of Buridan’s proposals, showing that his logic can be taken as more basic. In diesem Aufsatz betrachten wir das Geeignetsein einer modernen intervallbasierten temporalen Logik für die Modellierung von John Buridans Behandlung zeitabhängiger Sätze in seinen Sophismata. Aufbauend auf den Aufsatz stellen wir Buridans Analyse der temporalen Logik dar, mit besonderer Berücksichtigung seiner Begriffe der Negation und der absoluten/relativen Natur der Zukunft und der Vergangenheit. Wir führen einige standardmäßige moderne intervallbasierte temporale Aussagenlogiken ein, um zu illustrieren, wo Buridans intervallbasierte temporale Analyse von den standardmäßigen modernen Zugangsweisen abweicht. Wir geben formale Beweise einiger Behauptungen in an und skizzieren, wie die standardmäßigen modernen Systeme im Sinne der Vorschläge Buridans definiert werden könnten; wir zeigen damit, dass seine Logik als die grundlegendere aufgefasst werden kann. (shrink)

Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi ...

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...) makes the proposition true or makes its negation true. This chapter surveys a more general approach to logical semantics, known as possibility semantics, which replaces possible worlds with possibly partial "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset, as in set-theoretic forcing, or as compact regular open sets of an upper Vietoris space, as in the recent theory of "choice-free Stone duality." The elements of these sets, viewed as possibilities, may be partial in the sense of making a disjunction true without settling which disjunct is true. We explain how possibilities may be used in semantics for classical logic and modal logics and generalized to semantics for intuitionistic logics. The goals are to overcome or deepen incompleteness results for traditional semantics, to avoid the nonconstructivity of traditional semantics, and to provide richer structures for the interpretation of new languages. (shrink)

In this paper we look at the suitability of modern interval-based temporal logic for modeling John Buridan’s treatment of tensed sentences in his Sophismata. Building on the paper [Øhrstrøm 1984], we develop Buridan’s analysis of temporal logic, paying particular attention to his notions of negation and the absolute/relative nature of the future and the past. We introduce a number of standard modern propositional interval temporal logics to illustrate where Buridan’s interval-based temporal analysis differs from the standard modern approaches. We give (...) formal proofs of some claims in [Øhrstrøm 1984], and sketch how the standard modern systems could be defined in terms of Buridan’s proposals, showing that his logic can be taken as more basic. (shrink)