Related papers: Resolving G\"odel's Incompleteness Myth: Polynomia…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
G\"odel proved in the 1930s in his famous Incompleteness Theorems that not all statements in mathematics can be proven or disproven from the accepted ZFC axioms. A few years later he showed the celebrated result that Cantor's Continuum…
From the perspective of the physics of complex systems (1) we deal with the current state of modern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context;…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
During the last centuries of human history, many questions was repeated in connection with the great problems of the existence and origin of human beings, and also of the Universe. The old questions of common sense and philosophy have not…
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…
G\"odel's first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin's incompleteness theorem and a very…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
From the perspective of the physics of complex systems (1) we deal with the current state of mod-ern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context;…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
If we apply an extension of the Deduction meta-Theorem to Goedel's meta-reasoning of "undecidability", we can conclude that Goedel's formal system of Arithmetic is not omega-consistent. If we then take the standard interpretation…
In this paper we present a new proof of Solovay's theorem on arithmetical completeness of G\"odel-L\"ob provability logic GL. Originally, completeness of GL with respect to interpretation of $\Box$ as provability in PA was proved by R.…
In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking.…
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…