Hypergraph Basic Categorial Grammars

Pshenitsyn, Tikhon

doi:10.1007/978-3-030-51372-6_9

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…Our desire to introduce the weak Greibach normal form appeared due to another research about hypergraph basic categorial grammars (we presented a paper [10] about them at ICGT-2020); in that work we introduce a new approach to describing graph languages and prove that each grammar in this new formalism can be transformed into an equivalent HRG in the WGNF and vice versa. Theorems 1 and 2 show that ibHCFL is exactly the class of languages generated by grammars in the weak Greibach normal form; thus we also answer a question about the recognizing power of hypergraph basic categorial grammars -they also generate exactly ibHCFL.…”

Section: Resultsmentioning

confidence: 99%

Weak Greibach Normal Form for Hyperedge Replacement Grammars

Pshenitsyn

2020

Electron. Proc. Theor. Comput. Sci.

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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 wellknown Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they do not cover a large class of hypergraph languages (e.g. languages consisting of star graphs). In this paper, we introduce a weak Greibach normal form, whose definition corresponds to the lexicalized normal form for string grammars, and prove that every context-free hypergraph language (with nonsubstantial exceptions) can be generated by a grammar in this normal form. The proof presented in this paper generalizes a corresponding one for string grammars with a few more technicalities. * The study was funded by RFBR, project number 20-01-00670.

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Section: Resultsmentioning

confidence: 99%

Weak Greibach Normal Form for Hyperedge Replacement Grammars

Pshenitsyn

2020

Electron. Proc. Theor. Comput. Sci.

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“…Since there are such cases in linguistics where we need to work with graphs rather than with strings, we would like to generalize the categorial point of view discussed in Section 1 to hypergraphs. Our first attempt was a generalization of basic categorial grammars to hypergraphs; the resulting formalism called hypergraph basic categorial grammar was introduced at ICGT 2020 [10]. However, this formalism did not significantly improve our insight since most results were proved in the same way as for strings; in particular, such grammars generate the same set of languages as HRGs (with some nonsubstantial exceptions related to the number of isolated nodes).…”

Section: Hypergraph Lambek Calculusmentioning

confidence: 99%

Grammars Based on a Logic of Hypergraph Languages

Pshenitsyn

2021

Electron. Proc. Theor. Comput. Sci.

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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 by HRGs. We introduce a formalism that turns out to be more powerful than HRGs while having the same algorithmic complexity (NPcomplete). Namely, we introduce hypergraph Lambek grammars; they are based on the hypergraph Lambek calculus, which may be considered as a logic of hypergraph languages. We explain the underlying principles of hypergraph Lambek grammars, establish their basic properties, and show some languages of unbounded connectivity that can be generated by them (e.g. the language of all graphs, the language of all bipartite graphs, the language of all regular graphs).

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“…Being impressed by many similarities between HRGs and CFGs, we were curious whether it is possible to generalize type-logical grammars to hypergraphs. We started with basic categorial grammars and introduced hypergraph basic categorial grammars (see [17]); we showed their duality with HRGs and also a number of similarities with basic categorial grammars. Our goal now is to do the same with the Lambek calculus.…”

Section: Introductionmentioning

confidence: 99%

Hypergraph Lambek Calculus

Pshenitsyn

2020

Preprint

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It is known that context-free grammars can be extended to generating 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 (L) and grammars based on it to graphs. The resulting approach is called hypergraph Lambek calculus (HL). It is a logical sequential calculus whose sequents are graphs; it naturally extends the Lambek calculus and also allows one to embed its variants (commutative L, NL♦, L * 1 ). Besides, many properties of the Lambek calculus (cut elimination, counters, models) can be lifted to HL. However, while Lambek grammars are equivalent to context-free grammars in the string case, hypergraph Lambek grammars are much more powerful than hyperedge replacement grammars. Particularly, the former can generate the language of all graphs without isolated nodes; the language of all bipartite graphs; finite intersections of languages generated by hyperedge replacement grammars. Nevertheless, the derivability problem in HL and the membership problem for grammars based on HL are NP-complete as well as the membership problem for hyperedge replacement grammars.⋆ The study was funded by RFBR, project number 20-01-00670.

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Hypergraph Basic Categorial Grammars

Cited by 4 publications

References 9 publications

Weak Greibach Normal Form for Hyperedge Replacement Grammars

Weak Greibach Normal Form for Hyperedge Replacement Grammars

Grammars Based on a Logic of Hypergraph Languages

Hypergraph Lambek Calculus

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