# Stanislav SperanskiRussian Academy of Sciences | RAS · Steklov Mathematical Institute

Stanislav Speranski

PhD (in Logic)

## About

22

Publications

1,809

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114

Citations

Introduction

Additional affiliations

September 2016 - present

**St. Petersburg State University**

Position

- Professor

January 2014 - August 2016

**Sobolev Institute of Mathematics**

Position

- Researcher

July 2013 - January 2014

**Sobolev Institute of Mathematics**

Position

- Junior Scientific Researcher

## Publications

Publications (22)

We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s inte...

We introduce infinitary action logic with exponentiation—that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules (contraction, weakening, permutation). The logic is presented in the form of an infinitary sequent calculus. We prove cut el...

The idea of treating negation as a modality manifests itself in various logical systems, especially in Došen’s propositional logic $\textsf {N}$, whose negation is weaker than that of Johansson’s minimal logic. Among the interesting extensions of $\textsf {N}$ are the propositional logics $\textsf {N}^{\ast }$ and $\textsf {Hype}$; the former was p...

We shall be concerned with the modal logic BK | which is based on the Belnap{Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding strong negation'. Though all four values truth', falsity', neither' and both' are employed in its Kripke semantics, only the first two are expressible as terms. We sh...

The paper contains a survey on the complexity of various truth hierarchies arising in Kripke’s theory. I present some new arguments, and use them to obtain a number of interesting generalisations of known results. These arguments are both relatively simple, involving only the basic machinery of constructive ordinals, and very general.

We introduce infinitary action logic with exponentiation---that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules (contraction, weakening, permutation). The logic is presented in the form of an infinitary sequent calculus. We prove cut...

Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.

Inspired by Kit Fine's theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke's, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.

We shall be concerned with the modal logic BK — which is based on the Belnap-Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding `strong negation'. Though all four values `truth', `falsity', `neither' and `both' are employed in its Kripke semantics, only the first two are expressible as terms....

Inspired by Hintikka's ideas on constructivism, we are going to `effectivize' the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph `The Principles of Mathematics Revisited'. First we show that Nelson's realizability interpretation — which ex...

In this article we describe a bunch of
probability logics with quantifiers over events
, and develop primary techniques for proving computational complexity results (in terms of
m
-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of inter...

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with `strong negation'. We carry out a systematic study of the lattice of logics containing BK based on:
— introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics;
— assigning to every normal modal log...

Let σ be a signature and U a σ-structure with domain ℕ. Say that a monadic second-order σ-formula is ∏n¹ iff it has the form ∀X1∃X2∀X3⋯ XnΨ with X1,⋯ , Xn set variables and Ψ containing no set quantifiers. Consider the following properties: ACP for each positive integer n, the set of ∏n¹-σ-sentences true in U is ∏n¹-complete; ADP for each positive...

Many important achievements of formal logic have been concerned with the discovery of incomputability—and thus firmly rooted in the undecidability of the halting problem and its complement. Also, the latter produce influental examples of Σ 1 0 Σ10- and Π 1 0 Π10-complete sets, in modern terminology. Changing the focus from modelling computations to...

In a rather general setting, we prove a number of basic theorems concerning computational complexity of derivability in adaptive logics. For that setting, the so-called standard format of adaptive logics is suitably adapted, and the corresponding completeness results are established in a very uniform way.

We developed an original approach to cognition, based on the previously developed theory of neural modeling fields and dynamic logic. This approach is based on the detailed analysis and solution of the problems of artificial intelligence – combinatorial complexity and logic and probability synthesis. In this paper we interpret the theory of neural...

In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability,
then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated.
We prove, among other things, the Π 1 1 Π11-completeness for the general validity and...

We obtain a bunch of principal results on Belnapian modal algebras (henceforth called BK-lattices) — these results may serve as a semantical basis for further investigation of the lattice of extensions of Belnapian modal logic (denoted by BK here).

We carry out a study of definability issues in the standard models of Presburger and Skolem arithmetics (henceforth referred to simply as Presburger and Skolem arithmetics, for short, because we only deal with these models, not the theories, thus there is no risk of confusion) supplied with free unary predicates—which are strongly related to defina...

We study hierarchies of validity problems for prefix fragments in probability logic with quantifiers over propositional formulas, denoted
$ \mathcal{Q}\mathcal{P}\mathcal{L} $
, and its versions. It is proved that if a subfield
$ \mathfrak{F} $
of reals is definable in the standard model of arithmetic by a secondorder formula without set quanti...

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e. CLuN supplied with the reliability strategy and the minimal abnormality...

A language for reasoning about probability is generalized by adding quantifiers over propositional formulas to the language.
Then relevant decidability issues are considered. In particular, the results presented demonstrate that a rather weak fragment
of the new language has an undecidable validity problem. On the other hand, it is stated that a re...