Compact Bilinear Logic , introduced by Lambek [14], arises from the multiplicative fragment of Noncommutative Linear Logic of Abrusci [1] by identifying times with par and 0 with 1. In this paper, we present two sequent systems for CBL and prove the cut-elimination theorem for them. We also discuss a connection between cut-elimination for CBL and the Switching Lemma from [14].

In this paper, we present a computational algebraic representation of Hindi syntax. This paper is the first attempt to establish the representation of various facets of Hindi syntax into algebra, including dual nominative/ergative behavior, a syntacto-semantic case system and complex agreement rules between the noun and verb phrase. Using the pregroup analysis framework, we show how we represent morphological type reduction for morphological behavior of lexical markers, the representation of causative constructions which are morphologically affixed, as well as of light (...) verb constructions which form the verb by joint predication. We present examples adapted from the Hindi Dependency Treebank to show the pregroup analysis of Hindi sentences. (shrink)

We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).

We know from the literature in theoretical linguistics that interrogative constructions in Italian have particular syntactic properties, due to the liberal word order and the rich inflectional system. In this paper we show that the calculus of pregroups represents a flexible and efficient computational device for the analysis and derivation of Italian sentences and questions. In this context the distinction between direct vs. indirect statements and questions is explored.

Involutive Nonassociative Lambek Calculus is a nonassociative version of Noncommutative Multiplicative Linear Logic, but the multiplicative constants are not admitted. InNL adds two linear negations to Nonassociative Lambek Calculus ; it is a strongly conservative extension of NL Logical aspects of computational linguistics. LNCS, vol 10054. Springer, Berlin, pp 68–84, 2016). Here we also add unary modalities satisfying the residuation law and De Morgan laws. For the resulting logic InNLm, we define and study phase spaces. We use them to prove (...) the cut elimination theorem for a one-sided sequent system for InNLm, introduced here. Phase spaces are also employed in studying auxiliary systems InNLm, assuming the k-cyclic law for negation. The latter behave similarly as Classical Nonassociative Lambek Calculus, studied in de Groote and Lamarche :355–388, 2002) and Buszkowski. We reduce the provability in InNLm to that in InNLm. This yields the equivalence of type grammars based on InNLm with -free) context-free grammars and the PTIME complexity of InNLm. (shrink)