In a remarkable paper antedating Linear Logic by five years, Grishin (1983) presents a number of extensions of the Lambek calculus with the common characteristic that derivability holds between hypotheses A1,…,An, taken together by means of a multiplicative conjunction, and multiple conclusions B1,…,Bm, combined by means of a multiplicative disjunction. Linguistic exploration of Grishin's ideas has started in recent years.  In this section, we introduce a multiple-conclusion categorial system that is already well-studied: LG (for Lambek-Grishin calculus).  We present syntax and relational semantics of the system; in the next section, we turn to its computational interpretation.