Tikhon Pshenitsyn- Master of Science
- PhD Student at Russian Academy of Sciences
Tikhon Pshenitsyn
- Master of Science
- PhD Student at Russian Academy of Sciences
About
31
Publications
809
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
33
Citations
Introduction
Skills and Expertise
Current institution
Education
September 2017 - June 2023
Publications
Publications (31)
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it is sound and complete with respect to formal language semantics. This paper studies a similar relation between first-order intu...
We investigate complexity of the uniform membership problem for hyperedge replacement grammars in comparison with other mildly context-sensitive grammar formalisms. It turns out that the complexity of the problem considered depends heavily on how one defines a hypergraph. There are two commonly used definitions in the field which differ in whether...
В работе доказывается, что замыкающий ординал оператора непосредственной выводимости в инфинитарной логике действий равен $\omega^\omega$; тем самым дан ответ на открытый вопрос из статьи (С. Л. Кузнецов, С. О. Сперанский, 2022) о нахождении точного значения этой теоретико-доказательственной характеристики. Также в работе доказывается, что замыкающ...
The class of all $\ast$-continuous Kleene algebras, whose description includes an infinitary condition on the iteration operator, plays an important role in computer science. The complexity of reasoning in such algebras - ranging from the equational theory to the Horn one, with restricted fragments of the latter in between - was analyzed by Kozen (...
In 2023, Kuznetsov and Speranski introduced infinitary action logic with multiplexing $!^{m}\nabla \textrm{ACT}_{\omega }$ and proved that the derivability problem for it lies between the $\omega $ level and the $\omega ^{\omega }$ level of the hyperarithmetical hierarchy. We prove that this problem is $\varDelta ^{0}_{\omega ^{\omega }}$-complete...
In this paper, we introduce an extension of the Lambek calculus by optional divisions (\(\textrm{L}_{opt}\)). Namely, the right optional division \(A \angle B\) is defined as \(A \wedge (A/B)\), and the left one is defined as \(A \wedge (B \backslash A)\). A possible linguistic motivation to consider the new operations is describing verbs with opti...
Hypergraph Lambek grammars (HL-grammars) is a novel logical approach to generating graph languages based on the hypergraph Lambek calculus. In this paper, we establish a precise relation between HL-grammars and hypergraph grammars based on the double pushout (DPO) approach: we prove that HL-grammars generate the same class of languages as DPO gramm...
Lambek categorial grammars is a class of formal grammars based on the Lambek calculus. Pentus proved in 1993 that they generate exactly the class of context-free languages without the empty word. In this paper, we study categorial grammars based on the Lambek calculus with the permutation rule LP. Of particular interest is the product-free fragment...
We study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the non-emptiness problem for fusion grammars and the membership problem for fusion grammars without markers and connecto...
The multimodal Lambek calculus is an extension of the Lambek calculus that includes several product operations (some of them being commutative or/and associative), unary modalities, and corresponding residual implications. In this work, we relate this calculus to the hypergraph Lambek calculus HL. The latter is a general pure logic of residuation d...
We study how to relate well-known hypergraph grammars based on the double pushout (DPO) approach and grammars over the hypergraph Lambek calculus HL (called HL-grammars). It turns out that DPO rules can be naturally encoded by types of HL using methods similar to those used by Kanazawa for multiplicative-exponential linear logic. In order to genera...
Boolean grammars is a formalism introduced in [Okhotin, 2004], which extends well-known context-free grammars by conjunction and negation. Unlike context-free grammars, defining what language is generated by a Boolean grammar is hard. In [Okhotin, 2004], two possible ways of doing this are presented, namely, the semantics of the unique solution in...
In [Van Benthem, 1991] it is proved that all permutation closures of context-free languages can be generated by grammars over the Lambek calculus with the permutation rule (LP-grammars); however, to our best knowledge, it is not established whether converse holds or not. In this paper, we show that LP-grammars are equivalent to linearly-restricted...
In the graph grammar theory, there is a natural generalization of the context-free grammar approach to graphs called hyperedge replacement grammar (HRG). The latter is based on the hyperedge replacement procedure, and it preserves main principles and properties of context-free grammars (e.g. the pumping lemma). In the string case, there is an alter...
The hyperedge replacement grammar (HRG) formalism is a natural and well-known generalization of context-free grammars. HRGs inherit a number of properties of context-free grammars, e.g. the pumping lemma. This lemma turns out to be a strong restriction in the hypergraph case: it implies that languages of unbounded connectivity cannot be generated b...
We enrich the Lambek calculus with the cyclic shift operation, which is expected to model the closure operator of formal languages with respect to cyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination. Secondly, we turn to categorial grammars based on this calculus and show that they can generate non-context-free languages;...
We consider two approaches to generating formal string languages: context-free grammars and Lambek grammars, which are based on the Lambek calculus. They are equivalent in the sense that they generate the same set of languages (disregarding the empty word). It is well known that context-free grammars can be generalized to hyperedge replacement gram...
In this paper hypergraph Lambek calculus ($\mathrm{HL}$) is presented. This formalism aims to generalize the Lambek calculus ($\mathrm{L}$) to hypergraphs as hyperedge replacement grammars extend context-free grammars. In contrast to the Lambek calculus, $\mathrm{HL}$ deals with hypergraph types and sequents; its axioms and rules naturally generali...
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they d...
It is known that context-free grammars can be extended to generate graphs resulting in graph grammars; one of such fundamental approaches is hyperedge replacement grammars. On the other hand there are type-logical grammars which also serve to describe string languages. In this paper, we investigate how to extend the Lambek calculus $\mathrm{L}$ and...
This work is an attempt to generalize categorial grammars, which deal with string languages, to hypergraphs. We consider a particular approach called basic categorial grammar (BCG) and introduce its natural extension to hypergraphs --- hypergraph basic categorial grammar (HBCG). We show that BCGs can be naturally embedded in HBCGs. It turns out tha...
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they d...
In this paper we investigate formal properties of the Lambek calculus enriched with two new connectives named optional divisions (ODLC). Linguistic motivation to add them is describing optional arguments of verbs, e.g. the book in Tim reads the book. We present two theorems regarding recognizing power of the ODLC; in particular, we show that finite...
