Nominal tense logic and other sorted intensional frameworks

This thesis introduces of a system of tense logic called nominal tense logic (NTL), and several extensions. Its primary aim is to establish that these systems are logically interesting, and can provide useful models of natural language tense, temporal reference, and their interaction. Languages of nominal tense logic are a simple augmentation of Priorean tense logic. They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like propositional variables, nominals are atomic sentences and may be freely combined with other wffs using the usual connectives. When interpreting these languages we handle the Priorean components standardly, but insist that nominals must be true at one and only one time. We can think of nominals as naming this time. Logically, the change increases the expressive power of tensed languages. There are certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed in Priorean languages; with nominals they can. The effects of this increase in expressive power on the usual model theoretic results for tensed languages discussed, and completeness and decidability results for several temporally interesting classes of frames are given. Various extensions of the basic system are also investigated and similar results are proved. In the final chapter a brief treatment of similarly referential interval based logics is presented. As far as natural language semantics is concerned, the change is an important one. A familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal reference, it cannot provide realistic models of natural language temporal usage. Natural language tense is at least partly about referring to times, and nowadays the deictic and anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment of certain temporally referring expressions such as indexicals, and simple discourse phenomena

A topological perspective for branching-time logics

Questa tesi è suddivisa in due parti: - nella prima parte, abbiamo descritto la *Logica Temporale* e, in particolare, alcune logiche del tempo ramificato; - nella seconda parte abbiamo analizzato da un punto di vista topologico alcune proprietà algebriche degli alberi, su cui sono basate molte semantiche per la logica temporale. L'obiettivo principale della Logica temporale è la definizione di un linguaggio formale (e di una semantica) che possa esprimere proposizioni con tempi verbali, come "Ha piovuto", "Ho dormito, in passato", "In futuro impareremo a volare". Si osserva immediatamente che il valore di verità di queste proposizioni dipende dal momento in cui sono considerate, a differenza delle proposizioni della Logica Classica. Perciò, il primo passo per una definizione di verità in questo contesto è quello di costruire una adeguata struttura matematica che rappresenti il tempo. Nei primi due capitoli, analizzeremo varie scelte sintattiche e semantiche per la Logica Temporale, e differenti assunzioni ontologiche (una su tutte, l'*Indeterminismo*) che modificheranno il modello del tempo considerato. Seguendo l'articolo *Topological Aspects of Branching-Time Semantics *(2003) di M. Sabbadin e A. Zanardo, nel terzo capitolo abbiamo preso in considerazione una semantica inusuale per la Logica Temporale, basata su una naturale struttura topologica aggiunta alla semantica Ockhamista. In particolare, lo spazio dei rami massimali (o storie) della rappresentazione ad albero del tempo diventa uno spazio topologico *non-Archimedeo*. In questo capitolo vengono analizzate in dettaglio le proprietà di questo spazio, e viene dimostrato un importante risultato di validità. Infine il quarto capitolo, che è in parte un lavoro di ricerca, contiene la "traduzione" in questo nuovo linguaggio topologico di varie proprietà algebriche degli alberi. Vengono descritte le proprietà topologiche dello spazio delle storie degli alberi lineari, degli alberi finitamente ramificati, di quelli ben fondati, e di altre classi più particolari, come gli alberi ω-cofinali e gli alberi *jointed*. Il capitolo si conclude con un'analisi degli alberi di Souslin e degli alberi speciali, strettamente collegati al noto *Problema di Souslin*

Tense, aspect and temporal reference

English exhibits a rich apparatus of tense, aspect, time adverbials and other expressions that can be used to order states of affairs with respect to each other, or to locate them at a point in time with respect to the moment of speech. Ideally one would want a semantics for these expressions to demonstrate that an orderly relationship exists between any one expression and the meanings it conveys. Yet most existing linguistic and formal semantic accounts leave something to be desired in this respect, describing natural language temporal categories as being full of ambiguities and indeterminacies, apparently escaping a uniform semantic description. It will be argued that this anomaly stems from the assumption that the semantics of these expressions is directly related to the linear conception of time familiar from temporal logic or physics - an assumption which can be seen to underly most of the current work on tense and aspect. According to these theories, the cognitive work involved in the processing of temporal discourse consists of the ordering of events as points or intervals on a time line or a set of time lines. There are, however, good reasons for wondering whether this time concept really is the one that our linguistic categories are most directly related to; it will be argued that a semantics of temporally referring expressions and a theory of their use in defining the temporal relations of events require a different and more complex structure underlying the meaning representations than is commonly assumed. A semantics will be developed, based on the assumption that categories like tense, aspect, aspectual adverbials and propositions refer to a mental representation of events that is structured on other than purely temporal principles, and to which the notion of a nucleus or consequentially related sequence of preparatory process, goal event and consequent state is central. It will be argued that the identification of the correct ontology is a logical preliminary to the choice of any particular formal representation scheme, as well as being essential in the design of natural language front-ends for temporal databases. It will be shown how the ontology developed here can be implemented in a database that contains time-related information about events and that is to be queried by means of natural language utterances

The actual future is open

Open futurism is the indeterministic position according to which the future is 'open,' i.e., there is now no fact of the matter as to what future contingent events will actually obtain. Many open futurists hold a branching conception of time, in which a variety of possible futures exist. This paper introduces two challenges to (branching-time) open futurism, which are similar in spirit to a challenge posed by Kit Fine to (standard) tense realism. The paper argues that, to address the new challenges, open futurists must (i) adopt an objective, non-perspectival notion of actuality and (ii) subscribe to an A-theoretic, dynamic conception of reality. Moreover, given a natural understanding of "actual future," (iii) open futurism is naturally coupled with the view that a unique, objectively actual future exists, contrary to a common assumption in the current debate. The paper also contends that recognising the existence of a unique actual future helps open futurists to avoid potential misconceptions

Testing and debugging functional reactive programming

Many types of interactive applications, including video games, raise particular challenges when it comes to testing and debugging. Reasons include de-facto lack of reproducibility and difficulties of automatically generating suitable test data. This paper demonstrates that certain variants of Functional Reactive Programming (FRP) implemented in pure functional languages can mitigate such difficulties by offering referential transparency at the level of whole programs. This opens up for a multi-pronged approach for assisting with testing and debugging that works across platforms, including assertions based on temporal logic, recording and replaying of runs (also from deployed code), and automated random testing using QuickCheck. The approach has been validated on real, non-trivial games implemented in the FRP system Yampa through a tool providing a convenient Graphical User Interface that allows the execution of the code under scrutiny to be controlled, moving along the execution time line, and pin-pointing of violations of assertions on PCs as well as mobile platforms

The Invisible Thin Red Line

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world

Temporal logics

We consider a number of temporal logics, some interval-based and some instant-based, and the choices that have to be made if we need to construct a computational framework for such a logic. We consider the axiomatisation of the accessibility relations of the underlying temporal structures when we are using a modal language as well as the formulation of axioms for distinguishing concepts like actions, events, processes and so on for systems using first-order languages. Finally, we briefly discuss the fields of application of temporal logics and list a number of fields that looks promising for further research.Computer Science and Information SystemsM.Sc.(Computer Science

Temporal Operators and (Metaphysical) Presentism

In a paper titled “Tense, Modality, and Semantic Values,” (Philosophical Perspectives, 2003) Jeffrey King argues (in part) that tenses in English do not function as sentential operators but that they are more akin to object-language quantifiers over times. Although not an explicit concern of King’s in the paper under consideration here, his analysis poses several prima facie difficulties for the metaphysical position known as “presentism” (that is, roughly, the view that only what exists at the present is real). Specifically, the commonsense motivation for presentism is threatened because of the discrepancy King proposes between how tense actually functions in the language and how presentism typically insists that tense functions. Additionally, if King is right, the typical presentist paraphrasing project is seemingly jeopardized. Herein we will try to raise some worries about King’s proposal (e.g., without limitation, that he has failed to consider relevant potential sorts of operators) and about the cited linguistic evidence (e.g., that it is too parochial, turns on hard cases, etc.). Finally, we will suggest defenses (e.g., a Matti Eklund-inspired sort of indifferentism ) of both the motivation for presentism and the paraphrasing methods usually employed (which defenses arguably hold up even if King is correct)

Some Pioneering Formal Reconstructions of Diodorus' Master Argument

The article deals with some current pioneering formal reconstructions and interpretations of the problem well known in antiquity as The Master Argument. This problem is concerning with enrichment of formal logical systems with modal and temporal notions. The opening topic is devoted to reconstruction of Arthur Prior. while the other here included approach to the problem arc mostly reactions. revisions or additions to this one