Andrey Kudinov - Academia.edu (original) (raw)

Papers by Andrey Kudinov

Mathematics

We axiomatize strictly positive fragments of modal logics with the confluence axiom. We consider ... more We axiomatize strictly positive fragments of modal logics with the confluence axiom. We consider unimodal logics such as K.2, D.2, D4.2 and S4.2 with unimodal confluence ⋄□p→□⋄p as well as the products of modal logics in the set K,D,T,D4,S4, which contain bimodal confluence ⋄1□2p→□2⋄1p. We show that the impact of the unimodal confluence axiom on the axiomatisation of strictly positive fragments is rather weak. In the presence of ⊤→⋄⊤, it simply disappears and does not contribute to the axiomatisation. Without ⊤→⋄⊤ it gives rise to a weaker formula ⋄⊤→⋄⋄⊤. On the other hand, bimodal confluence gives rise to more complicated formulas such as ⋄1p∧⋄2n⊤→⋄1(p∧⋄2n⊤) (which are superfluous in a product if the corresponding factor contains ⊤→⋄⊤). We also show that bimodal confluence cannot be captured by any finite set of strictly positive implications.

Cornell University - arXiv, May 26, 2014

We consider modal logics of products of neighborhood frames and prove that for any pair L and L o... more We consider modal logics of products of neighborhood frames and prove that for any pair L and L of logics from set {S4, D4, D, T} modal logic of products of L-neighborhood frames and L-neighborhood frames is the fusion of L and L .

Cornell University - arXiv, Oct 29, 2021

We consider quantified pretransitive Horn modal logic. It is known that such logics are complete ... more We consider quantified pretransitive Horn modal logic. It is known that such logics are complete with respect to predicate Kripke frames with expanding domains. In this paper we prove that they are also complete with respect to neighbourhood frames with constant domains.

We study logics with expressible transitive closure modality (pretransitive logics). In such logi... more We study logics with expressible transitive closure modality (pretransitive logics). In such logics we can express formulas of finite depth. We prove the finite model property for a family of pretransitive logics of finite depth. There is an old problem about decidability of logics Kmn = K+2 mp → 2np, where 2m is the sequence of m boxes. For the case when m ≤ 1 or n ≤ 1, and for the trivial case m = n the finite model property (FMP) is known. As for the other cases it is unknown whether Kmn has FMP or even if it is decidable. If n> m then the logic Kmn is pretransitive 1, which means that we can express the truth in a point-generated submodel. Formally, L is pretransitive if there exists a formula χ(p) with a single variable p such that for any Kripke model M with M L and for any w in M we have M, w χ(p) ⇔ ∀u(wR∗u ⇒ M, u p), where R ∗ is the transitive reflexive closure of the accessibility relation of M. It is known [2] that L is pretransitive iff for some k ≥ 0 it contains the ...

We consider modal logics of products of neighborhood frames and find the modal logic of all produ... more We consider modal logics of products of neighborhood frames and find the modal logic of all products of normal neighborhood frames.

EPiC Series in Computing

We study derivational modal logic of real line with difference modality and prove that it has fin... more We study derivational modal logic of real line with difference modality and prove that it has finite model property but does not have finite axiomatization.

Logic Journal of the IGPL, 2018

The paper considers modal logics of products of neighbourhood frames. The n-product of modal logi... more The paper considers modal logics of products of neighbourhood frames. The n-product of modal logics is the logic of all products of neighbourhood frames of the corresponding logics. We find the n-product of any two pretransitive Horn axiomatizable logics. As a corollary, we find the d-logic of products of topological spaces from some classes of topological spaces.

Izvestiya: Mathematics, 2017

Аннотация В работе доказана финитная аппроксимируемость и разрешимость одного семейства модальных... more Аннотация В работе доказана финитная аппроксимируемость и разрешимость одного семейства модальных логик. Бинарное отношение R назовём предтранзитивным, если R * = ∪ i m R i для некоторого m 0, где R * транзитивное рефлексивное замыкание R. Под высотой шкалы (W, R) будем понимать высоту предпорядка (W, R *). Описаны специальные разбиения (фильтрации) предтранзитивных шкал конечной высоты, из чего следует финитная аппроксимируемость и разрешимость их модальных логик.

Russian Mathematical Surveys, 2016

We consider propositional modal logic with two modal operators Box\BoxBox and D\DD. In topological se... more We consider propositional modal logic with two modal operators Box\BoxBox and D\DD. In topological semantics Box\BoxBox is interpreted as an interior operator and D\DD as difference. We show that some important topological properties are expressible in this language. In addition, we present a few logics and proofs of f.m.p. and of completeness theorems. Comment: Advances in Modal Logic, Volume 6, 2006

With a set S of words in an alphabet A we associate the frame (S,H), where sHt iff s and t are wo... more With a set S of words in an alphabet A we associate the frame (S,H), where sHt iff s and t are words of the same length and h(s,t)=1 for the Hamming distance h. We investigate some unimodal logics of these frames. We show that if the length of words n is fixed and finite, the logics are closely related to many-dimensional products S5 n , so in many cases they are undecidable and not finitely axiomatizable. The relation H can be extended to infinite sequences. In this case we prove some completeness theorems characterizing the well-known modal logics DB and TB in terms of the Hamming distance.

Lecture Notes in Computer Science, 2013

In this paper we introduce public announcements to Subset Space Logic (SSL). In order to do this ... more In this paper we introduce public announcements to Subset Space Logic (SSL). In order to do this we have to change the original semantics for SSL a little and consider a weaker version of SSL without the cross axiom. We present an axiomatization, prove completeness and show that this logic is PSPACE-complete. Finally, we add the arbitrary announcement modality which expresses "true after any announcement", prove several semantic results, and show completeness for a Hilbert-style axiomatization of this logic. Proposition 23. Let ϕ be a formula. For all Γ ∈ S u , we have for all finite sequences (ψ 1 ,. .. , ψ n) of formulas, F s , θ s , ([Γ ] ≡ u , f (Γ)) |= [ψ 1 ]. .. [ψ n ]ϕ iff M u , Γ |= [ψ 1 ]. .. [ψ n ]ϕ.

$Research paper thumbnail of О топологической модальной логике <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">\mathbb R</annotation></semantics></math>R с неравенством$

Успехи математических наук, 2008

Outstanding Contributions to Logic, 2014

In this chapter we study modal logics of topological spaces in the combined language with the der... more In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces, T1-spaces, dense-in-themselves spaces, a zerodimensional dense-in-itself separable metric space, R n (n ≥ 2). We also discuss the correlation between languages with different combinations of the topological, the derivational, the universal and the difference modality in terms of definability.