In this paper we address the decision problem for a fragment of unquantified formulae of real analysis, which, besides the operators of Tarski’s theory of reals, includes also strict and non-strict predicates expressing comparison, monotonicity, concavity, and convexity of continuous real functions over possibly unbounded intervals. The decision result is obtained by proving that a formula of o...

Nowadays academia and industry use model checkers. These tools use search-based algorithms to check the satisfaction of some property f in M . Formally, M |= f , where M is a transition system representation of a specification written in a language L. Such a representation may come from the semantics of L. This paper presents a rapid prototyping of a model checker development strategy for Circu...

Solving simple arithmetic word problems is one of the challenges in Natural Language Understanding. This paper presents a novel method to learn to use formulas to solve simple arithmetic word problems. Our system, analyzes each of the sentences to identify the variables and their attributes; and automatically maps this information into a higher level representation. It then uses that representa...

Explosive increase in end-user computing on distributed systems requires that end-users develop application software by themselves. One solution is given as a formula of “a domain model = a computation model.” This formula implies that one task in a domain model of cooperative work corresponds to one object in a computation model based on an object-oriented model. Application development enviro...

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requir...

Readability formulas are methods used to match texts with the readers’ reading level. Several methodological paradigms have previously been investigated in the field. The most popular paradigm dates several decades back and gave rise to well known readability formulas such as the Flesch formula (among several others). This paper compares this approach (henceforth ”classic”) with an emerging par...

The logic called ATL (Alternating-time Temporal Logic) was introduced, in 1997, as a modal logic of agents. The first direct algorithm to test whether a given ATL-formula θ is satisfiable was provided by V. Goranko and G. van Drimmelen in 2006. Their algorithm is based on alternating infinite tree automata. In 2009, V. Goranko and D. Shkatov proposed a method to test satisfiability of a formula...

We interpret walks in the first quadrant with steps {(1, 1), (1, 0), (−1, 0), (−1,−1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks using the steps above, beginning and ending at the origin. We give an explicit formula for a restricted class of such words using a correspondence between such words and Dyck pa...

Alloy is a automatically analyzable modelling language based on first-order logic. An Alloy model can be translated into a Boolean formula whose satisfying assignments correspond to instances in the model. Currently, the translation procedure mechanically converts each piece of the Alloy model individually into its most straightforward Boolean representation. This thesis proposes a more efficie...