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Prior’s tonk, notions of logic, and levels of inconsistency: vindicating the pluralistic unity of science in the light of categorical logical positivism
There are still on-going debates on what exactly is wrong with Prior’s pathological “tonk.” In this article I argue, on the basis of categorical...
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The Role of Symmetry in Mathematics
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry...
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Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models
In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent...
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Categorical Semantics of Linear Logic for All
This note compares several notions of categorical model of intuitionistic linear logic in the literature. The emphasis is on explaining why choices...
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Modes of Adjointness
The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural...
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Branching Space-Times and Parallel Processing
There is a remarkable similarity between some mathematical objects used in the Branching Space-Times framework and those appearing in computer...
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Paraconsistency in Categories: Case of Relevance Logic
Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant...
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Picturing classical and quantum Bayesian inference
We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent...
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Semantic Vector Models and Functional Models for Pregroup Grammars
We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an...
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Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples
The development of “operational quantum logic” points out that classical Boolean structures are too rigid to describe the actual and potential...
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MODELING RELATIONS
In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does...
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Proofs as Efficient Programs
Logic and theory of computation have been intertwined since their first days. The formalized notion(s) of effective computation are at first...
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A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity
A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and...
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Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches
For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and...
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Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness
A categorical ontology of space and time is presented for emergent biosystems, super-complex dynamics, evolution and human consciousness. Relational...
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A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems
A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal...
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Quasi-varieties: A special access
Quasi-equational logic concerns with a completeness theorem, i. e. a list of general syntactical rules such that, being given a set of graded...
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Playful, Streamlike Computation
We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation — that is, computation of...