Results

**1 - 4**of**4**###
Memoization for *Unary* Logic Programming: *Characterizing* *PTIME*

"... We give a characterization of deterministic polyno-mial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. More precisely, we study the restriction of this framework to ..."

Abstract
- Add to MetaCart

We give a

*characterization*of deterministic polyno-mial time computation based on an algebraic structure called the*resolution*semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. More precisely, we study the restriction of this framework### Proof Complexity of Relativized Statements

, 2012

"... The first-order formulas that do not have finite models give rise to uniform families of propositional unsatisfiable formulas, one for each finite cardinality. Motivated by the question of characterizing the class of such formulas whose propositional translations have short resolution refutations, w ..."

Abstract
- Add to MetaCart

The first-order formulas that do not have finite models give rise to uniform families of propositional unsatisfiable formulas, one for each finite cardinality. Motivated by the question of

*characterizing*the class of such formulas whose propositional translations have short*resolution*refutations### Author manuscript, published in "ICDT (2012) 46-60" Highly Expressive Query Languages for Unordered Data Trees ∗

, 2012

"... We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay ..."

Abstract
- Add to MetaCart

We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay of different factors: the expressive power of basic queries, the embedding of computation into data (as in Active XML), and the use of deterministic vs. nondeterministic control. All languages are Turing complete, but not necessarily query complete in the sense of Chandra and Harel. Indeed, we show that some combinations of features yield serious limitations, analogous to FO k definability in the relational context. On the other hand, the limitations come with benefits such as the existence of powerful normal forms. Other languages are “almost ” complete, but fall short because of subtle limitations reminiscent of the copy elimination problem in object databases.

### Chapter 12 Rough Sets and Rough Logic: A KDD Perspective

"... Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of con ..."

Abstract
- Add to MetaCart

Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of con-cepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, proper-ties, relations etc.) not completely but by means of their reflections (i.e. approx-imations) in the chosen language. The most important issues in this induction process are: – construction of relevant primitive concepts from which approximations of more complex concepts are assembled, – measures of inclusion and similarity (closeness) on concepts, – construction of operations producing complex concepts from the primitive ones.

**1 - 4**of

**4**