Related papers: Axiomatizing mathematical conceptualism in third o…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Computational modeling is a critical tool for understanding consciousness, but is it enough on its own? This paper discusses the necessity for an ontological basis of consciousness, and introduces a formal framework for grounding…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: modal systems in which cognitive contexts extend known facts with hypothetical assumptions in order to explore their consequences.…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…
We consider a set-theoretic version of mereology based on the inclusion relation $\subseteq$ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of $\in$ from $\subseteq$, we identify…
Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…
In conceptual modeling (CM) as a subdiscipline of software engineering, current proposed ontologies (categorical analysis of entities) are typically established through whole adoption of philosophical theories (e.g. Bunge s). In this paper,…
This paper examines conceptual models and their application to computational thinking. Computational thinking is a fundamental skill for everybody, not just for computer scientists. It has been promoted as skills that are as fundamental for…
There is an ongoing debate in computer science how algorithms should best be studied. Some scholars have argued that experimental evaluations should be conducted, others emphasize the benefits of formal analysis. We believe that this debate…
There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…
In general, providing an axiomatization for an arbitrary logic is a task that may require some ingenuity. In the case of logics defined by a finite logical matrix (three-valued logics being a particularly simple example), the generation of…