Related papers: On sequents of $\Sigma$ formulas
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
We consider strong combinatorial principles for sigma-directed families of countable sets in the ordering by inclusion modulo finite, e.g. P-ideals of countable sets. We try for principles as strong as possible while remaining compatible…
We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form "If $\sim A$, then $A$", should not hold,…
To what extent can our limited set of observations be used to pin down the specifics of a ``Theory of Everything''? In the limit where the links are arbitrarily tenuous, a ``Theory of Everything'' might become a ``Theory of Anything''. A…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so…
In this paper, we study the employment of $\Sigma_1$-sentences with certificates, i.e., $\Sigma_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is…
We prove that Solovay's set $\Sigma$ is generic over the ground model via a forcing notion whose order relation $\subseteq$-extends the given order relation.
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
In this paper the notion of a superconformal structure on a supermanifold is introduced in an effort to study the superparticle sigma-model. There are, in particular, two main aspects of the sigma-model which are investigated. The first is…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…