Conditional sentences with quantifying expressions are systematically ambigous. In one reading, the if -clause restricts the domain of the overt quantifier; in the other, the if -clause restricts the domain of a covert quantifier, which defaults to epistemic necessity. Although the ambiguity follows directly from the LewisKratzer line on if, it is not generally acknowledged, which has led to ps...

In this paper we prove that there exists a Horn clause H such that the problem: given a Horn clause G. Is G a consequence of H ? is not recursive. Equivalently, there exists a one-clause PROLOG program such that there is no PROLOG implementation answering TRUE if the program implies a given goal and FALSE otherwise. We give a short survey of earlier results concerning clause implication and pro...

We report a polynomial time SAT problem instance, the Blocked SAT problem. A blocked clause set, an instance of the Blocked SAT problem, contains only blocked clauses. A close is blocked (for resolution) if it has a literal on which no resolution is possible in the clause set. We know from work of O. Kullmann that a blocked clause can be added or deleted from a clause set without changing its s...

This paper discusses a special kind of syntax-semantics mismatch: a noun with a relative clause is interpreted as if it were a complement clause. An analysis in terms of Lexical Resource Semantics is developed which provides a uniform account for “normal” relative clauses and for the discussed type of relative clause.

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...

penalty clause or liquidated damage which is formerly agreed between parties is legally examined and accepted as a rule. although judge could in some circumstances modify this stipulation. yet its economic analysis which is focused on economic efficiency can be considered as a “major unexplained puzzle in the economic theory of law”. this article compares the major legal systems in the case of ...

Conjunctive Normal Form (CNF) Boolean formulas generated from resolution or solution enumeration often have much redundancy. It is desirable to have an efficient algorithm to simplify and compact such CNF formulas on the fly. Given a clause in a CNF formula, if a subset of its literals constitutes another clause in the formula, then the first clause is said to be subsumed by the second clause. ...

The first convincing demonstration that local search could be used to solve challenging satisfiability problems was provided by the GSAT algorithm [9]. GSAT performs gradient descent search in the space of complete truth assignments, where adjacent assignments differ on a single variable and the objective function is the number of clauses not satisfied by the assignment. Like all local search r...

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the s...

On these elements, clause (1.b) is immediate: if C[Ṽ ] is a value, then also C[W̃ ] is a value and they are in E. This is sufficient, because E∈ X . Clause (1.a) is proved by an induction on C. The details are easy: the only possible case is C = C1C2; we use the fact that if λx.P E λx.Q, and V E W , and E ∈ Y , then (P{V/x}, Q{W/x}) ∈ XE′ for some E ′ with E ⊆ E ′, which follows from the definit...