Tense Logic and Ontology of Time

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are developed, and mapped to the ontology of time.Peer reviewe

The Everett-Wheeler interpretation and the open future

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new (though I expect correction on this), but they are natural and intuitive, and relate to traditional naive ideas of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open.Comment: 11 page

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

Temporal Reasoning and MAS

In this paper we investigate if it is possible and useful to reason about time within social/normative multi-agent systems (MAS) by taking into account the general guidelines of tense logic. We focus on the combination of special-purpose logics: we provide a formal account in which a minimal temporalization helps in reasoning about time in an abstract way. We also explore a new variant of deontic tense logic by using a hybrid tense logic. The accounts provided allow to model temporal provisions within both particular norms and general legal principles, and also help in the detection of breaches of good faith and confidence.Facultad de Ciencias Jurídicas y SocialesFacultad de Informátic

Philosophical lessons of entanglement

The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern scientific thought. There are two kinds of statements about the world: those made from inside the world, and those from outside. The conflict between contradictory statements which both appear to be true can be resolved by recognising that they are made in different perspectives. Probability, in an objective sense, belongs in the internal perspective, and to statements in the future tense. Such statements obey a many-valued logic, in which the truth values are identified as probabilities.Comment: Talk given at 75 Years of Quantum Entanglement, Kolkata, India, 10 January 201

The metaphysics of time investigations in tense-logic and a B-series semantics

Includes bibliographical references (leaves 81-83).The view that time flows from the future to the present and then recedes into the past is both natural and deeply problematic. So called 'A-theories' about time claim that this is the fundamental nature of temporality. This is not the view which will be defended in this paper. Rather I shall argue for what is known as a 'B-theory' analysis of time and language, one in which the relations of 'earlier than' and 'later than' are necessary and sufficient for any analysis of time. The structure of this paper is tripartite. The first part will address the philosophical and metaphysical tenets of both the A and B-theories of time. In this section, McTaggart's 1908 argument for the unreality of time will be presented along with some objections to it. I will show that some seemingly convincing arguments against 'McTaggart's paradox' are unsuccessful and his paradox does indeed call the A-series into question. This section will lay the groundwork for further discussions relating to other disciplines which are concerned with this debate by describing the issues and points of tension

Time and tense in English

It has not been my aim to provide conclusive evidence for or against anyone hypothesis regarding Time and Tense. I have simply attempted to collect together and collate much of what has been written on the topic of tense in English, in order to show what the current trends of thought are. In Chapter One I presented a brief survey of some of the more basic notions associated with time and tense, in order to provide a background for the more linguistic approach to follow. I therefore examined such issues as the difference between time and tense, the problem of the passage and directionality of time, of the present moment, time and space , tense as a universal, "and various features of tense systems. I sketched Bull's system of scalars, vectors and axes as representative of our English tense system. Chapter Two dealt with time and logic, but as I am a mere layman in matters logical, I refrained from discussing any individual logical system in depth, and rather discussed various problems which appear to confront the logician in formulating a tensed or tenseless logic. This chapter aimed at providing a better understanding of the linguistic issues to follow, for time and logic are intimately connected with language. Chapter Three was more linguistically oriented, and in it I attempted to provide a broad outline of the development of thoughts about tense before the Transformationalist period (pre 1960). Because of the vast scope involved, I had, perforce, to be brief at times. I gave attention to tense in classical grammatical studies, and summarized how it was seen from about 1500 to 1800. I gave more detailed treatment to the twentieth century, focussing specifically on grammarians like Jespersen (1933), Twaddell (1960), Ota (1963), Palmer (1965) and others - all, writers typical of the structuralist era. At the end of Chapter Three I provided an overall summary of ideas on the main tenses by the end of the structuralist period - ideas which were to change radically within the next few years. In Chapter Four I discussed the ideas of tense of some of the main transformationalist/generativists - Diver (1964), Crystal (1966), Huddlestone (1968), Gallagher (1970), McCawley (1971) and Seuren (1974), in an attempt to show how theories on tense were becoming increasingly abstract, and how most data indicated that it is highly probable that tense is an abstract higher predicate of the sentence in which it appears in surface structure, closely related to temporal adverbs. Chapter Five continued in the same vein. I tried to show, using syntactic tests, that tense is a higher predicate, and used arguments involving Conjunction Reduction (based on Kiparsky (1968)), VP Constituency, Sequence of Tense, Pronominalization, and Quantification. In Chapter Six I focussed more closely on tense-time adverbials, in order to show that they have the same syntactic properties as tense, are also probably deep superordinate predicates, and are closely related to tense. My suggestion was that either tense is derived from temporal adverbs or vice versa, as this would simplify the grammar. The derivation procedures at the end of the chapter (6.8) were largely based on Hausmann (1971). I made no detailed reference to extralinguistic matters which affect tenses, in this study - such factors as are diScussed by G. Lakoff (1971) (presuppositions and relative well-formedness) and by R. Lakoff (1975). Tense is not a matter of pure Structuralism, just as language is not - extralinguistic factors ought to be accounted for before any study can claim to be conclusive. For this reason I do not in any way claim to have made an exhaustive study of time and tense - I have simply attempted to summarize and coordinate thoughts on the subject, and to suggest tentatively that the most adequate grammar of English would probably derive tense from underlying temporal adverbs

Strong Completeness and the Finite Model Property for Bi-Intuitionistic Stable Tense Logics

Bi-Intuitionistic Stable Tense Logics (BIST Logics) are tense logics with a Kripke semantics where worlds in a frame are equipped with a pre-order as well as with an accessibility relation which is ‘stable’ with respect to this pre-order. BIST logics are extensions of a logic, BiSKt, which arose in the semantic context of hypergraphs, since a special case of the pre-order can represent the incidence structure of a hypergraph. In this paper we provide, for the first time, a Hilbert-style axiomatisation of BISKt and prove the strong completeness of BiSKt. We go on to prove strong completeness of a class of BIST logics obtained by extending BiSKt by formulas of a certain form. Moreover we show that the finite model property and the decidability hold for a class of BIST logics