We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable is there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiabi...

A clause is a disjunction of literals. We use set notation; a set of literals denotes the clause that is their disjunction. The empty clause is denoted by . The width of a clause C, denoted |C|, is the number of literals in it. The width of a CNF formula F , denoted width(F ), is the maximum width of any clause in F . For a partial assignment ρ, C|ρ denotes the restriction of the clause C by ap...

Clause recommendation is the problem of recommending a clause to legal contract, given context contract in question and type which should belong. With not much prior work being done toward generation contracts, this was proposed as first step bigger generation. As an open-ended text problem, distinguishing characteristics lie nature language sublanguage considerable similarity textual content w...

ion property for the main clause is greater than or equal to the cardinality of the than clause property. The latter is obtained by taking the boolean meet of the property corresponding to the common noun argument of the hypothetical determiner in the than clause and the noun-phrase abstraction property of the than clause. So our example would be paraphraseable as: ‘the number of books bought b...

In Danish relative clauses and embedded interrogative clauses are not extraction islands. However, there is an asymmetry between the two clauses. In Danish it is possible to extract the subject out of an embedded interrogative clause. Extraction of the subject out of a relative clause, on the other hand, is not allowed. In this paper we present a formal HPSG analysis of extraction in Danish whi...