This paper introduces some notions concerning binary relations according to [9]. It is also an attempt to complement the knowledge contained in the Mizar Mathematical Library regarding binary relations. We define here an image and inverse image of element of set A under binary relation of two sets A, B as image and inverse image of singleton of the element under this relation, respectively. Nex...

This report is a rst attempt of formalizing the diagonalization proof technique. We give a strategy how to systematically construct diagonalization proofs: (i) nding an indexing relation, (ii) constructing a diagonal element, and (iii) making the implicit contradiction of the diagonal element explicit. We suggest a declarative representation of the strategy and describe how it can be realized i...

The last few years have seen an opening up of what is considered to be the legitimate terrain of international relations (IR). This move is, for the most part, extremely welcome. Yet, the multiple theoretical and empirical openings in IR since the end of the Cold War have failed to elucidate many of the puzzles, questions and problems posed by the contemporary conjuncture. There are a number of...

Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). A complete classification of all HS fr...

the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitr...

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel es...

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel es...

We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeomet-ric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan's 1 ψ 1 summation and a very-well-poised 4 ψ 6 summation as spec...

5 Sets and Functions 1 5.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 5.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 5.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 5.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.6 Congr...

We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan’s 1ψ1 summation and a very-well-poised 4ψ6 summation as special c...