11 research outputs found

    Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)

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    We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises agent-centric proof theories that are negation-complete (maximal) and consistent (and hence strictly weaker than, for example, Peano Arithmetic) and enjoy the disjunction property (like Intuitionistic Logic). In other words, internalised proof theories are ultrafilters and all internalised proof goals are definite in the sense of being either provable or disprovable to an agent by means of disjunctive internalised proofs (thus also called epistemic deciders). Still, LDiiP itself is classical (monotonic, non-constructive), negation-incomplete, and does not have the disjunction property. The price to pay for the negation completeness of our interactive proofs is their non-monotonicity and non-communality (for singleton agent communities only). As a normal modal logic, LDiiP enjoys a standard Kripke-semantics, which we justify by invoking the Axiom of Choice on LiiP's and then construct in terms of a concrete oracle-computable function. LDiiP's agent-centric internalised notion of proof can also be viewed as a negation-complete disjunctive explicit refinement of standard KD45-belief, and yields a disjunctive but negation-incomplete explicit refinement of S4-provability.Comment: Expanded Introduction. Added Footnote 4. Corrected Corollary 3 and 4. Continuation of arXiv:1208.184

    Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)

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    We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs effect a durable epistemic impact in the possibly adversarial communication medium CM (which is imagined as a distinguished agent), and only in that, that consists in the permanent induction of the perfect and thus disjunctive knowledge of their proof goal by means of CM's knowledge of the proof: If CM knew my proof then CM would persistently and also disjunctively know that my proof goal is true. So intuitionistic interactive proofs effect a lasting transfer of disjunctive propositional knowledge (disjunctively knowable facts) in the communication medium of multi-agent distributed systems via the transmission of certain individual knowledge (knowable intuitionistic proofs). Our (necessarily) CM-centred notion of proof is also a disjunctive explicit refinement of KD45-belief, and yields also such a refinement of standard S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP, and their internalised notions of proof. As a side-effect, we offer a short internalised proof of the Disjunction Property of Intuitionistic Logic (originally proved by Goedel).Comment: continuation of arXiv:1201.3667; extended start of Section 1 and 2.1; extended paragraph after Fact 1; dropped the N-rule as primitive and proved it derivable; other, non-intuitionistic family members: arXiv:1208.1842, arXiv:1208.591

    Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

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    We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively

    Mechanised metamathematics : an investigation of first-order logic and set theory in constructive type theory

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    In this thesis, we investigate several key results in the canon of metamathematics, applying the contemporary perspective of formalisation in constructive type theory and mechanisation in the Coq proof assistant. Concretely, we consider the central completeness, undecidability, and incompleteness theorems of first-order logic as well as properties of the axiom of choice and the continuum hypothesis in axiomatic set theory. Due to their fundamental role in the foundations of mathematics and their technical intricacies, these results have a long tradition in the codification as standard literature and, in more recent investigations, increasingly serve as a benchmark for computer mechanisation. With the present thesis, we continue this tradition by uniformly analysing the aforementioned cornerstones of metamathematics in the formal framework of constructive type theory. This programme offers novel insights into the constructive content of completeness, a synthetic approach to undecidability and incompleteness that largely eliminates the notorious tedium obscuring the essence of their proofs, as well as natural representations of set theory in the form of a second-order axiomatisation and of a fully type-theoretic account. The mechanisation concerning first-order logic is organised as a comprehensive Coq library open to usage and contribution by external users.In dieser Doktorarbeit werden einige Schlüsselergebnisse aus dem Kanon der Metamathematik untersucht, unter Verwendung der zeitgenössischen Perspektive von Formalisierung in konstruktiver Typtheorie und Mechanisierung mit Hilfe des Beweisassistenten Coq. Konkret werden die zentralen Vollständigkeits-, Unentscheidbarkeits- und Unvollständigkeitsergebnisse der Logik erster Ordnung sowie Eigenschaften des Auswahlaxioms und der Kontinuumshypothese in axiomatischer Mengenlehre betrachtet. Aufgrund ihrer fundamentalen Rolle in der Fundierung der Mathematik und ihrer technischen Schwierigkeiten, besitzen diese Ergebnisse eine lange Tradition der Kodifizierung als Standardliteratur und, besonders in jüngeren Untersuchungen, eine zunehmende Bedeutung als Maßstab für Mechanisierung mit Computern. Mit der vorliegenden Doktorarbeit wird diese Tradition fortgeführt, indem die zuvorgenannten Grundpfeiler der Methamatematik uniform im formalen Rahmen der konstruktiven Typtheorie analysiert werden. Dieses Programm ermöglicht neue Einsichten in den konstruktiven Gehalt von Vollständigkeit, einen synthetischen Ansatz für Unentscheidbarkeit und Unvollständigkeit, der großteils den berüchtigten, die Essenz der Beweise verdeckenden, technischen Aufwand eliminiert, sowie natürliche Repräsentationen von Mengentheorie in Form einer Axiomatisierung zweiter Ordnung und einer vollkommen typtheoretischen Darstellung. Die Mechanisierung zur Logik erster Ordnung ist als eine umfassende Coq-Bibliothek organisiert, die offen für Nutzung und Beiträge externer Anwender ist

    Second Generation General System Theory: Perspectives in Philosophy and Approaches in Complex Systems

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    Following the classical work of Norbert Wiener, Ross Ashby, Ludwig von Bertalanffy and many others, the concept of System has been elaborated in different disciplinary fields, allowing interdisciplinary approaches in areas such as Physics, Biology, Chemistry, Cognitive Science, Economics, Engineering, Social Sciences, Mathematics, Medicine, Artificial Intelligence, and Philosophy. The new challenge of Complexity and Emergence has made the concept of System even more relevant to the study of problems with high contextuality. This Special Issue focuses on the nature of new problems arising from the study and modelling of complexity, their eventual common aspects, properties and approaches—already partially considered by different disciplines—as well as focusing on new, possibly unitary, theoretical frameworks. This Special Issue aims to introduce fresh impetus into systems research when the possible detection and correction of mistakes require the development of new knowledge. This book contains contributions presenting new approaches and results, problems and proposals. The context is an interdisciplinary framework dealing, in order, with electronic engineering problems; the problem of the observer; transdisciplinarity; problems of organised complexity; theoretical incompleteness; design of digital systems in a user-centred way; reaction networks as a framework for systems modelling; emergence of a stable system in reaction networks; emergence at the fundamental systems level; behavioural realization of memoryless functions

    Technology in an Alternative Modernity

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    This essay tries to defend a general embracing-controlling-stance on modern technology on the basis of the analysis of technology and a synthesized theory about the relationship between technology and culture. The task is carried out in the framework of an alternative modernity theory, in a cross-cultural context. China and specific technologies are used to illustrate the central ideas as case studies

    Characterising and modeling the co-evolution of transportation networks and territories

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    The identification of structuring effects of transportation infrastructure on territorial dynamics remains an open research problem. This issue is one of the aspects of approaches on complexity of territorial dynamics, within which territories and networks would be co-evolving. The aim of this thesis is to challenge this view on interactions between networks and territories, both at the conceptual and empirical level, by integrating them in simulation models of territorial systems.Comment: Doctoral dissertation (2017), Universit\'e Paris 7 Denis Diderot. Translated from French. Several papers compose this PhD thesis; overlap with: arXiv:{1605.08888, 1608.00840, 1608.05266, 1612.08504, 1706.07467, 1706.09244, 1708.06743, 1709.08684, 1712.00805, 1803.11457, 1804.09416, 1804.09430, 1805.05195, 1808.07282, 1809.00861, 1811.04270, 1812.01473, 1812.06008, 1908.02034, 2012.13367, 2102.13501, 2106.11996

    Ambivalent Sovereignty: Inquiries into the Dual Foundation of Political Realism\u27s Subject

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    Ambivalent Sovereignty inquires into the subject of political realism. This subject, sovereign authority, appears to have a dual foundation. It appears divided against itself, but how can realism nonetheless observe legitimate modes of sovereignty emerge? Against the liberal idea that a synthesis of both material-coercive and ideal-persuasive powers should be accomplished, within the world of international relations, realism gives meaning to a structural type of state power that is also constitutionally and legitimately dividing itself--against itself. Machiavelli but particularly also other realists such as Hannah Arendt, Max Weber, and Aristotle are being reinterpreted to demonstrate why each state\u27s ultimate authority may symbiotically emerge from its self-divisions, rather than from one synthetic unity. Whereas liberal theorists, from Montesquieu to John Rawls and Alexander Wendt, err too far in assuming the presence of the state\u27s monistic authority, the realist theorists further advance an answer to how sovereign states may begin to both recognize and include only the most-legitimate manifestations of their common dualist authority. Ambivalent Sovereignty is relevant in this sense as it transcends-and-yet-includes these common dualities: freedom/necessity; emergence/causation; self-organization/power structures

    CORPORATE SOCIAL RESPONSIBILITY IN ROMANIA

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    The purpose of this paper is to identify the main opportunities and limitations of corporate social responsibility (CSR). The survey was defined with the aim to involve the highest possible number of relevant CSR topics and give the issue a more wholesome perspective. It provides a basis for further comprehension and deeper analyses of specific CSR areas. The conditions determining the success of CSR in Romania have been defined in the paper on the basis of the previously cumulative knowledge as well as the results of various researches. This paper provides knowledge which may be useful in the programs promoting CSR.Corporate social responsibility, Supportive policies, Romania
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