In theory and practice of modern SAT solving, clause-elimination procedures are essential for simplifying formulas in conjunctive normal form (CNF). Such procedures identify redundant clauses and faithfully remove them, either before solving in a preprocessing phase or during solving, resulting in a considerable speed up of the SAT solver. A wide number of effective clause-elimination procedure...

The problem of finding a small unsatisfiable core of an unsatisfiable CNF formula is addressed. The proposed algorithm, Trimmer , iterates over each internal node d in the resolution graph that ‘consumes’ a large number of clauses M (i.e. a large number of original clauses are present in the unsat core only for proving d) and attempts to prove them without the M clauses. If this is possible, it...

This study reconsiders the acquisition of relative clauses based on data from two sentencerepetition tasks. Using materials modeled on the relative constructions of spontaneous child speech, we asked four-year-old Englishand German-speaking children to repeat six different types of relative clauses. Although English and German relative clauses are structurally very different, the results were s...

1 Introduction 2 Defining conditionals 2.1 What is a conditional? 2.2 The marking of conditionals 3 Structural issues 3.1 The position of merger of the if-clause 3.1.1 If-clauses as adverbial clauses 3.1.2 Height of attachment 3.1.3 A source for sentence-initial if-clauses 3.2 Clause-internal syntax of the if-clause 3.2.1 The location of if 3.2.2 The conditional–interrogative link 3.2.3 The abs...

Temporal verification of universal (i.e., valid for all computation paths) properties of various kinds of programs, e.g., procedural, multi-threaded, or functional, can be reduced to finding solutions for equations in form of universally quantified Horn clauses extended with well-foundedness conditions. Dealing with existential properties (e.g., whether there exists a particular computation pat...

Max-SAT resolution is the adaption of the powerful SAT resolution rule for the Max-SAT problem. One of the differences between these two rules is that Max-SAT resolution adds, besides the resolvent, several compensation clauses to keep the formula’s equivalency. We address in this paper the problem of reducing both the number and the size of these compensation clauses. We show that the order in...

Preference logic programming (PLP) is an extension of constraint logic programming (CLP) for declaratively specifying problems requiring optimization or comparison and selection among alternative solutions to a query. In the PLP framework, the deenite clauses of a constraint logic program are augmented by two new kinds of clauses, which we call optimization clauses and arbiter clauses. Optimiza...

This paper presents complexity results about the satisfiability ofmodal Horn clauses for several modal propositional logics. Almost all these results are negative in the sense that restricting the input formula to modal Horn clauses does not decrease the inherent complexity of the satisfiability problem. We first show that, when restricted to modal Horn clauses, the satisfiability problem for a...

This paper examines the development of relative clauses in early child language. It is argued that relative clauses constitute a network of related constructions that children acquire in a piecemeal bottom-up way, starting with relative clauses that are only little different from simple sentences which are gradually extended into more complex grammatical patterns. The acquisition process is dri...