Two partial orders P = (X, S) and Q = (X, s’) are complementary if P fl Q = {(x, x): x E x} and the transitive closure of P U Q is {(x. y): x, y E X}. We investigate here the size w(n) of the largest set of pairwise complementary par!iai orders on a set of size n. In particular, for large n we construct L?(n/iogrt) mutually complementary partial orders of order n, and show on the other hand tha...

Introduction Conclusions References

For linear evolution control system described by ẋ = Ax(t) + Bu(t), x(0) = x0 (A generates a strongly continuous semigroup {S(t)}t≥0 on a Banach space X; B is a linear unbounded operator), the attainable set K (t) set is studied. Conditions of the independence of t for its closure K(t) are established. Controllability conditions for some classes of evolution systems are obtained.

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and simil...

1. Epistemic closure The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure (EC), has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that p, and she knows that p entails...