QBF Proof Complexity

Quantified Boolean Formulas (QBF) and their proof complexity are not as well understood as propositional formulas, yet remain an area of interest due to their relation to QBF solving. Proof systems for QBF provide a theoretical underpinning for the performance of these solvers. We define a novel calculus IR-calc, which enables unification of the principal existing resolution-based QBF calculi and applies to the more powerful Dependency QBF (DQBF). We completely reveal the relative power of important QBF resolution systems, settling in particular the relationship between the two different types of resolution-based QBF calculi. The most challenging part of this comparison is to exhibit hard formulas that underlie the exponential separations of the proof systems. In contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. To this end we exhibit a new proof technique for showing lower bounds in QBF proof systems based on strategy extraction. We also find that the classical lower bound techniques of the prover-delayer game and feasible interpolation can be lifted to a QBF setting and provide new lower bounds. We investigate more powerful proof systems such as extended resolution and Frege systems. We define and investigate new QBF proof systems that mix propositional rules with a reduction rule, we find the strategy extraction technique also works and directly lifts lower bounds from circuit complexity. Such a direct transfer from circuit to proof complexity lower bounds has often been postulated, but had not been formally established for propositional proof systems prior to this work. This leads to strong lower bounds for restricted versions of QBF Frege, in particular an exponential lower bound for QBF Frege systems operating with AC0[p] circuits. In contrast, any non-trivial lower bound for propositional AC0[p]-Frege constitutes a major open problem

Time granularity in simulation models within a multi-agent system

The understanding of how processes in natural phenomena interact at different scales of time has been a great challenge for humans. How information is transferred across scales is fundamental if one tries to scale up from finer to coarse levels of granularity. Computer simulation has been a powerful tool to determine the appropriate amount of detail one has to impose when developing simulation models of such phenomena. However, it has proved difficult to represent change at many scales of time and subject to cyclical processes. This issue has received little attention in traditional AI work on temporal reasoning but it becomes important in more complex domains, such as ecological modelling. Traditionally, models of ecosystems have been developed using imperative languages. Very few of those temporal logic theories have been used for the specification of simulation models in ecology. The aggregation of processes working at different scales of time is difficult (sometimes impossible) to do reliably. The reason is because these processes influence each other, and their functionality does not always scale to other levels. Thus the problems to tackle are representing cyclical and interacting processes at many scales and providing a framework to make the integration of such processes more reliable. We propose a framework for temporal modelling which allows modellers to represent cyclical and interacting processes at many scales. This theory combines both aspects by means of modular temporal classes and an underlying special temporal unification algorithm. To allow integration of different models they are developed as agents with a degree of autonomy in a multi-agent system architecture. This Ecoagency framework is evaluated on ecological modelling problems and it is compared to a formal language for describing ecological systems

The mathematicization of nature.

This thesis defends the Quine-Putnam indispensability argument for mathematical realism and introduces a new indispensability argument for a substantial conception of truth. Chapters 1 and 2 formulate the main components of the Quine-Putnam argument, namely that virtually all scientific laws quantify over mathematical entities and thus logically presuppose the existence thereof. Chapter 2 contains a detailed discussion of the logical structure of some scientific theories that incorporate or apply mathematics. Chapter 3 then reconstructs the central assumptions of Quine's argument, concluding (provocatively) that "science entails platonism". Chapter 4 contains a brief discussion of some major theories of truth, including deflationary views (redundancy, disquotation). Chapter 5 introduces a new argument against such deflationary views, based on certain logical properties of truth theories. Chapter 6 contains a further discussion of mathematical truth. In particular, non-standard conceptions of mathematical truth such as "if-thenism" and "hermeneuticism". Chapter 7 introduces the programmes of reconstrual and reconstruction proposed by recent nominalism. Chapters 8 discusses modal nominalism, concluding that modalism is implausible as an interpretation of mathematics (if taken seriously, it suffers from exactly those epistemological problems allegedly suffered by realism). Chapter 9 discusses Field's deflationism, whose central motivating idea is that mathematics is (pace Quine and Putnam) dispensable in applications. This turns on a conservativeness claim which, as Shapiro pointed out in 1983, must be incorrect (using Godel's Theorems). I conclude in Chapter 10 that nominalistic views of mathematics and deflationist views of truth are both inadequate to the overall explanatory needs of science

The Language of Paul Muldoon

This book interprets the multifarious writing of the Irish-American word wizard, Paul Muldoon, who has been described by The Times Literary Supplement as ‘the most significant English-language poet born since the second World War’. Readership: All interested in poetry and writing from Ireland and the English-speaking world, and in the enigma of language

Language as Ritual: Saying What Cannot Be Said with Western and Confucian Ritual Theories

This dissertation addresses one of the classical philosophical and theological problems of religious language, namely, how to speak meaningfully about matters that appear to be inexpressible. While addressed extensively in a variety of literatures across cultures, the problem persists, particularly in regard to harmonizing theological, philosophical, and linguistic perspectives. The dissertation argues that (i) language is best understood as a species of ritual; (ii) so understood, religious language speaks to and about religious realities subjunctively, that is, as if such realities could be talked about; and (iii) this way of understanding language achieves greater harmony among philosophical and linguistic approaches while achieving some degree of cross-cultural generality. The argument begins with a cross-cultural comparison between modern social scientific ritual theories, especially that of Roy A. Rappaport, and the Confucian ritual theory of Xunzi. This generates a novel theory of ritual capable of engaging theories of language that have emerged in modern linguistics, philosophy of language, logic, and hermeneutics. The semiotics of Charles Sanders Peirce provides the unifying framework for the theory, which leads to the first conclusion that language can be understood as a species of ritual. When language is understood as ritual, there are several options for interpreting religious speech as meaningful. An analysis of these alternatives on terms semantically demarcated by Hilary Putnam leads to the conclusion that language expresses theological insights in the same way it expresses anything else: as if reality and its elements were the way the language form and process construes and renders them. This analysis both advances critiques of language as understood under the linguistic turn, especially by Terrence W. Deacon and Daniel L. Everett, and establishes the second and third conclusions of the thesis

The 1995 Goddard Conference on Space Applications of Artificial Intelligence and Emerging Information Technologies

This publication comprises the papers presented at the 1995 Goddard Conference on Space Applications of Artificial Intelligence and Emerging Information Technologies held at the NASA/Goddard Space Flight Center, Greenbelt, Maryland, on May 9-11, 1995. The purpose of this annual conference is to provide a forum in which current research and development directed at space applications of artificial intelligence can be presented and discussed

A jurisprudential study: proving witchcraft in Africa

Widespread incidents of mob violence that are associated with witchcraft pose significant risks towards African criminal process. The need to address the extent to which these incidents threaten the overall institutional legitimacy of African criminal process constitutes the principal motivation behind the project of this thesis. This thesis identifies three major sets of challenges that are complained about by African communities. These pertain to (1) the relevant institutional practices that are to be followed in witchcraft cases (institutional); (2) the legal meaning of witchcraft (material); and (3) the evidential heuristics or processes of proof that are required to prove the direct crime of witchcraft (probative). These institutional, material and probative challenges are then summarised into a single overall thesis question: how can the direct crime of witchcraft be proven in Africa? This thesis embarks upon an Afrocentric Jurisprudential (theoretical) study in order to develop heuristics for the evidential proof of witchcraft in criminal cases in Africa. The kind of Jurisprudence undertaken in this thesis constitutes a prescriptive, middle-order level of theorising in that the proof heuristics that are developed take the form of argumentation schemes that are to be applied in witchcraft trials in Africa. The overall answer given to the main thesis question takes the form of an argument, a defeasible modus ponens, that is underpinned by a broad conception of (evidential) proof. The argument is that: (1) Generally speaking, if the relevant African institutional, material and probative (IMP) practices can be shown to be adhered to, then the plausibility of the evidential proof of the direct crime of witchcraft (P(w)) would have been established; (2) this thesis shows how the relevant IMP practices can be adhered to; (3) therefore, the plausibility of P(w) has been established by this thesis

A jurisprudential study: proving witchcraft in Africa

Widespread incidents of mob violence that are associated with witchcraft pose significant risks towards African criminal process. The need to address the extent to which these incidents threaten the overall institutional legitimacy of African criminal process constitutes the principal motivation behind the project of this thesis. This thesis identifies three major sets of challenges that are complained about by African communities. These pertain to (1) the relevant institutional practices that are to be followed in witchcraft cases (institutional); (2) the legal meaning of witchcraft (material); and (3) the evidential heuristics or processes of proof that are required to prove the direct crime of witchcraft (probative). These institutional, material and probative challenges are then summarised into a single overall thesis question: how can the direct crime of witchcraft be proven in Africa? This thesis embarks upon an Afrocentric Jurisprudential (theoretical) study in order to develop heuristics for the evidential proof of witchcraft in criminal cases in Africa. The kind of Jurisprudence undertaken in this thesis constitutes a prescriptive, middle-order level of theorising in that the proof heuristics that are developed take the form of argumentation schemes that are to be applied in witchcraft trials in Africa. The overall answer given to the main thesis question takes the form of an argument, a defeasible modus ponens, that is underpinned by a broad conception of (evidential) proof. The argument is that: (1) Generally speaking, if the relevant African institutional, material and probative (IMP) practices can be shown to be adhered to, then the plausibility of the evidential proof of the direct crime of witchcraft (P(w)) would have been established; (2) this thesis shows how the relevant IMP practices can be adhered to; (3) therefore, the plausibility of P(w) has been established by this thesis