Prolog systems currently work with the restriction that negative subgoals not contain free variables, although some authors have suggested that this restriction can be lifted by running the theorem prover to exhaustion on the subgoal being considered. We suggest that this approach is likely not to be computationally viable in practice, and describe and formalize a new approach to dealing with q...

(1) ∀u, k∀v ≤ρ tuk∃w A0(u, k, v, w), where A0 is a quantifier–free formula 1 (containing only u, k, v, w as free variables) in the language of a suitable subsystem T ω of arithmetic in all finite types, t is a closed term and ≤ρ is defined pointwise (ρ being an arbitrary finite type). Lets suppose that (1) is provable in T . Then from a given such proof one can extract an effective uniform boun...

We consider the monodic formulas of common knowledge predicate logic, which allow applications of epistemic operators to formulas with at most one free variable. We provide nite axiomatizations of the monodic fragment of the most important common knowledge predicate logics (the full logics are known to be not recursively enumerable) and single out a number of their decidable fragments. On the o...

A formula '(x 1 ; : : :; x n) conforms to a partition P of fx 1 ; : : :; x n g if it is equivalent to a Boolean combination of formulae that do not have free variables from more than one block of P. We show that if ' conforms to two partitions P 1 and P 2 , it also conforms to their greatest lower bound in the partition lattice. As a corollary, we obtain that the concept of orthographic dimensi...

The issue of the breakdown of the marriage bond in Western societies has become a routine object of social and moral concern, political and public debate. This is striking, given that in most non-western cultures still and in every society heretofore, marriage has been insisted upon as the required precondition for the mating of men and women as the act that initiates and sustains the family or...

This paper reports our ongoing research effort to develop a system which translates legal texts into logical forms in which we can check for inconsistency. Our logical formalization conforms to Davidsonian Style, which is suitable for languages allowing expressions with zero-pronouns such as Japanese. We examine our system with actual data of legal documents. As a result, the system was 78% of ...

Second-order uniication is undecidable in general. Miller showed that uniication of so-called higher-order patterns is decidable and unitary. We show that the uniication of a linear higher-order pattern s with an arbitrary second-order term that shares no variables with s is decidable and nitary. A few extensions of this uniication problem are still decidable: unifying two second-order terms, w...

Abstract. We give a new insight into the upper bounding of the 3-SAT threshold by the first moment method. The best criteria developed so far to select the solutions to be counted discriminate among neighboring solutions on the basis of uniform information about each individual free variable. What we mean by uniform information, is information which does not depend on the solution: e.g. the num...

We define a model of predicate logic in which every term and predicate, open or closed, has an absolute denotation independently of a valuation of the variables. For each variable a, the domain of the model contains an element JaK which is the denotation of the term a (which is also a variable symbol). Similarly, the algebra interpreting predicates in the model directly interprets open predicat...

Recently it has been argued that some of the fine-tuning problems of the MSSM inflation associated with the existence of a saddle point along a flat direction may be solved naturally in a class of supergravity models. Here we extend the analysis and show that the constraints on the Kähler potentials in these models are considerably relaxed when the location of the saddle point is treated as a f...