166 research outputs found

    Magyar nyelvjĂĄrĂĄsok 2023

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    Paraconsistent transition systems

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    Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined as providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.publishe

    Rethinking inconsistent mathematics

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    This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the rolee of logic and ethics in the practice of mathematics

    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

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    This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

    Time-Situated Metacognitive Agency and Other Aspects of Commonsense Reasoning

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    Much research in commonsense reasoning (CSR) involves use of external representations of an agent's reasoning, based on compelling features of classical logic. However, these advantages come with severe costs, including: omniscience, consistency, static semantics, frozen deadlines, lack of self-knowledge, and lack of expressive power to represent the reasoning of others. Active logic was developed to address many of these, but work to date still leaves serious gaps. The present work focuses on major extensions of active logic to deal with self-knowledge, and their implementation into a newly-developed automated reasoner for commonsense active logic. Dealing with self-knowledge has been designed and implemented in the reasoner via a new treatment of quotation as a form of nesting. More sophisticated varieties of nesting, particularly quasi-quotation mechanisms, have also been developed to extend the basic form of quotation. Active logic and the reasoner are applied to classical issues in CSR, including a treatment of one agent having the knowledge and inferential mechanisms to reason about another's time-situated reasoning

    Being and Historical Change in Hegel\u27s Science

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    This dissertation, Being and Historical Change in Hegel’s Science of Logic, examines the immanent relationship between metaphysics and history, specifically historical change, through an examination of Hegel’s Science of Logic. It seems to me that this relationship has been under-explored both in metaphysics broadly and Hegel scholarship specifically. For instance, many authors have discussed the role of history in Hegel’s philosophy and many others have focused on his metaphysics. But only a few have discussed how these two aspects immanently intersect with one another; specifically, what the examination of metaphysics can teach us about interpreting history and historical change. My motivation for the project is therefore rooted in answering two basic, interrelated questions: What kind of metaphysics must we articulate that accounts for historical change, where historical change is understood through the lens of contingent ‘ruptures’ with the past such as social/political revolutions or seemingly violent fractures in nature? And second, what must ‘being’ be like, or what primary metaphysical principle, helps us understand such changes? These are the questions that drew me to Hegel’s metaphysics in the Science of Logic. Specifically, I am interested in how Hegel conceives of the structured, intelligible reality of our lived experience not in terms of unity, at least not in the first place, but rather as the historical product of a dynamic tension that is inherent to reality itself. Accordingly, my thesis and contribution is that Hegel posits an element of difference and not identity/unity as the most basic metaphysical element which I further argue opens a space to interpret the conceptual structures that we use to make sense of the world as historically generated and thus open to being undermined, dissolved, and reconstituted. While many authors acknowledge a dynamic element to Hegel’s metaphysics few articulate it in terms of a principle of difference and even fewer in a way that accommodates historical change. Many authors have sought to reconcile such an antagonistic view of reality by arguing that Hegel’s metaphysics contains an implicitly presupposed foundational principle of identity that continuously reasserts itself through the apparent dynamism. This typically gets expressed via Hegel’s most famous category: the Concept. Examples of this include teleological accounts in which being unfolds conceptually through greater complexity in the world. Others take a more epistemic view, emphasizing a goal of developing through dialectic all the conceptual conditions regarding the unity and structure of objects in the world. My contribution is to turn this on its head, so to speak, by showing the inherent antagonism that forms the beginning not only remains throughout the account of the Logic, but that the Concept is in fact the most articulate expression of this principle of difference. The Concept therefore becomes our best category for understanding history as open to radical change in ways that teleological descriptions of history do not

    What is a Relevant Connective?

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    Paraconsistent resolution

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    Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for inconsistent theories, specializing to the classical semantics for the consistent ones. Direct (instead of refutational) reasoning with classical resolution is sound and complete for this semantics, when augmented with a specific weakening which, in particular, excludes Ex Falso. Dropping all forms of weakening yields reasoning which also avoids typical fallacies of relevance

    Diagram Reasoning and Paraconsistent Thinking: Hieromonk Hierotheos, His Ancestry, and Legacy

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    The article is dedicated to the use of logical diagrams in Byzantine Trinitarian theology. Logical diagrams are a kind of logical computation that is often considered to originate with Euler and Leibniz, but they were, in fact, used by Byzantine theologians since at least the ninth century. Nevertheless, logical diagrams were never so widely accepted as they began to be from the late thirteenth century to the early fifteenth century. The diagrams seem to have been introduced into Trinitarian theology by Eustratius of Nicaea (an authoritative philosopher who did not fare as well as a theologian) in his anti-Latin polemics dating to ca. 1112. From there, the use of diagrams was reclaimed in about the 1140s by the Latinophrone Nicetas “of Maroneia” and rejected in 1256 by the anti-Latin theologian Emperor Theodore II Laskaris. Nevertheless, beginning in the 1270s, their popularity and variability exploded. Eventually, triadological diagrams were “canonized” as the legacy of St. Hierotheos of Athens, the teacher of Dionysius the Areopagite, by Joseph Bryennios in the early fifteenth century. Even the “internal” opponent of Palamite theology, Theophanes of Nicaea, resorted to diagrams in defending his own triadology. The figure who rendered diagrams critical for the “Hesychast” theologians was, in the 1270s, hieromonk Hierotheos. He was able to express with diagrams the inconsistency of the mainstream Byzantine understanding of the Trinity. Nevertheless, his own name would come, in the fourteenth century, under a kind of damnatio memoriae, so that his main ideas circulated rather under the name of Hierotheos of Athens. This article argues that hieromonk Hierotheos passed from the Church of Patriarch Joseph to the Church of Patriarch Arsenius (or the Arsenites). Some of the highly authoritative teachers of the Palamites were in disagreement with the Great Church on the Arsenite issue, refusing to accept the act of 1410, where the Great Church had declared the Arsenites to be on the right side of the conflict. This fact could have affected the memory of hieromonk Hierotheos in the milieu where his works were most in demand. This research was supported by the University of Oxford project ‘New Horizons for Science and Religion in Central and Eastern Europe’ funded by the John Templeton Foundation. The opinions expressed in the publication are those of the author(s) and do not necessarily reflect the view of the John Templeton Foundation
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