Online research in philosophy

What is a temporal part? Most accounts explain it in terms of timeless parthood: a thing's having a part without temporal qualification. Some find this hard to understand, and thus find the view that persisting things have temporal parts--fourdimensionalism--unintelligible. T. Sider offers to help by defining temporal parthood in terms of a thing's having a part at a time. I argue that no such account can capture the notion of a temporal part that figures in orthodox four-dimensionalism: temporal parts must be timeless parts. This enables us to state four-dimensionalism more clearly.

It has long been recognized that temporal anaphora in French and English depends on the aspectual distinction between events and states. For example, temporal location as well as temporal update depends on the aspectual type. This paper presents a general theory of aspect-based temporal anaphora, which extends from languages with grammatical tenses (like French and English) to tenseless languages (e.g. Kalaallisut). This theory also extends to additional aspect-dependent phenomena and to non-atomic aspectual types, processes and habits, which license anaphora to proper atomic parts (cf. nominal pluralities and kinds).

If ordinary objects have temporal parts, then temporal predications have the following truth conditions: necessarily, ( a is F) at t iff a has a temporal part that is located at t and that is F. If ordinary objects have temporal counterparts, then, necessarily, ( a is F) at t iff a has a temporal counterpart that is located at t and that is F. The temporal-parts account allows temporal predication to be closed under the parthood relation: since all that is required to be F at t is to have a temporal part, a t , that is located at t and that is F, every object that has a t as a temporal part is F at t . Similarly for the temporal-counterparts account. Both closure under parthood and closure under counterparthood are shown to have unacceptable consequences. Then strategies for avoiding closure are considered and rejected.

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.

A semantics with plural entitles and plural times accounts for cumulative relations between plural arguments and temporal expressions. The semantics equips nominal, verbal and sentential meanings with temporal context variables and treats temporal modifiers as temporal generalized quantifiers; cumulative conjunction, however, takes place at types lower than generalized quantifiers. The mediation of temporal context variables allows cumulative relations to percolate between an argument in a main clause and one in a temporal clause, in apparent violation of locality restrictions. Plural times form a semilattice structure imposed on the set of intervals; no interaction is observed between this and the internal temporal structure of intervals.

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic system for this extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc.

Reasoning and talking about time is to a great extent reasoning and talking about what actually happens or might happen at some time or another. This is perhaps not crucial if our concern is with abstract temporal reasoners or planners intended for specific applications, but it arguably matters for the prospects of knowledge representation and natural language semantics. The variety of the world is the variety of the things that happen, and we can’t deal with it without taking events at face value (just as we cannot deal with physical bodies or masses by confining ourselves to their spatial coordinates). This is the stance we took in [11], where we argued that the notion of an event structure can be given an autonomous characterization germane to both common sense and natural language. In [12] and [13] we also showed that the formal connection between the way events are perceived to be ordered and the underlying temporal dimension is essentially that of a construction of a linear ordering from the basic formal ontological properties of a domain of events— specifically, mereological and topological properties. The purpose of this paper is to expand on this by further investigating the subtle connections between time and events. After a brief review, in the first part we shall generalize the notion of an event structure to that of a refinement structure, where various degrees of temporal granularity are accommodated. In the second part we shall then investigate how these structures can account for the context-dependence of temporal structures in natural language semantics.

The meanings of temporal adverbials seem easy to describe, but the compositional interaction with tense and aspect is notoriously difficult to analyse because we (more accurately: I) do not understand yet the principles governing the tense/aspect architecture of natural languages well enough. One of the most difficult areas of temporal structure is the perfect, and the literature quoted in this article shows that there is little agreement on its meaning(s). I believe that we will make progress only by a careful investigation of the meanings of temporal adverbials and by stating their formal semantics in a way which is precise enough to test empirical predictions. This is what the present article wants to do. It studies the interaction of the German durative temporal PP seit a ‘since a’ with tense, in particular with the perfect.