Session 17 Ecophysiology

n/

Addition theorems, DD-spaces and dually discrete spaces

summary:A {\it neighbourhood assignment\/} in a space $X$ is a family \Cal O= \{O_x:x\in X\} of open subsets of $X$ such that $x\in O_x$ for any $x\in X$. A set $Y\subseteq X$ is {\it a kernel of \Cal O\/} if \Cal O(Y)=\bigcup\{O_x:x\in Y\}=X. If every neighbourhood assignment in $X$ has a closed and discrete (respectively, discrete) kernel, then $X$ is said to be a $D$-space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf $P$-space is a $D$-space and we prove an addition theorem for metalindelöf spaces which answers a question of Arhangel'skii and Buzyakova

On the expressibility of Stable Logic Programming

Schlipf (Sch95) proved that Stable Logic Programming (SLP) solves all NP decision problems. We extend Schlipf’s result to prove that SLP solves all search problems in the class NP. Moreover, we do this in a uniform way as defined in (MT99). Specifically, we show that there is a single DATALOG ¬ program PTrg such that given any Turing machine M, any polynomial p with non-negative integer coefficients and any input σ of size n over a fixed alphabet Σ, there is an extensional database edbM,p,σ such that there is a one-to-one correspondence between the stable models of edbM,p,σ ∪PTrg and the accepting computations of the machine M that reach the final state in at most p(n) steps. Moreover, edbM,p,σ can be computed in polynomial time from p, σ and the description of M and the decoding of such accepting computations from its corresponding stable model of edbM,p,σ ∪ PTrg can be computed in linear time. A similar statement holds for Default Logic with respect to Σ P 2-search problems 1

Stable Models and an Alternative Logic Programming Paradigm

Stable model semantics appeared... In this paper we argue that rather than to try to resolve these inconsistencies and force stable model semantics into a standard logic programming mold (this effort most likely is doomed to failure), a change of view is required. Therefore, we propose a perspective on the stable model semantics that departs from several basic tenets of logic programming. At the same time, this perspective leads to a computational system very much in the general spirit of logic programming. The system is declarative..