The non-axiomatizability of the observational predicate calculus (generalized Trachtenbrot's theorems)
The observational predicate calculus and complexity of computations (Preliminary communication)
The Orthogonal Projection and the Riesz Representation Theorem
In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals...
The positivity problem for fourth order linear recurrence sequences is decidable
The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
The prime and maximal spectra and the reticulation of BL-algebras
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.
The problem of the additive generation of finitely-valued t-conorms.
The process of induction as a non-classical logic's double negation: evidence from classical scientific theories.
The Properties of Sets of Temporal Logic Subformulas
This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an...
The pseudovariety is hyperdecidable
The recursive sets in certain monadic second order fragments of arithmetic.
The resolution tableau for logics of likelihood
The second-order monadic theory of the free inverse monoid is undecidable. (La théorie monadique du second ordre du monoïde inversif libre est indécidable.)
The Soft Logic of Thomas Harriot
The strength of Turing determinacy within second order arithmetic
We investigate the reverse mathematical strength of Turing determinacy up to Σ₅⁰, which is itself not provable in second order arithmetic.
The study on semicopula based implications
Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...
The theory of abelian p-groups with the quantifier I is decidable
The theory of Archimedean real closed fields in logics with Ramsey quantifiers
The theory of boolean algebras with a distinguished subalgebra is undecidable
The theory of differentially closed fields in logics with cardinal quantifiers.
The Theory of Successor with an Extra Predicate.