Related papers: Axiomatizing mathematical conceptualism in third o…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
Semantic mapping is the incremental process of "mapping" relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on…
To provide a foundation for conceptual modeling, ontologies have been introduced to specify the entities, the existences of which are acknowledged in the model. Ontologies are essential components as mechanisms to model a portion of reality…
Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical…
Causal inference is a central goal across many scientific disciplines. Over the past several decades, three major frameworks have emerged to formalize causal questions and guide their analysis: the potential outcomes framework, structural…
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Conceptualization, a fundamental element of human cognition, plays a pivotal role in human generalizable reasoning. Generally speaking, it refers to the process of sequentially abstracting specific instances into higher-level concepts and…
As one of the longest-running computer-assisted formal mathematics projects, large tracts of mathematical knowledge have been formalized with the help of the Mizar system. Because Mizar is based on first-order classical logic and set…
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the…
Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…