### Table 1. Logical and physical algebras.

1999

"... In PAGE 3: ... Such an algebra is system-specific, meaning that different systems may implement the same data model and the same logical algebra, but may use different physical algebras [12]. Table1 shows the logical and the physical operators used by the conventional optimizer. We describe the physical algebra operators in more detail in section 3.... ..."

Cited by 7

### Table 1. Translations between logical and algebraic systems.

1997

"... In PAGE 11: ... Composing the translations arising from the Burris-McKenzie approach with those arising from algebraisation yields a further two translations from rst- order logic to quasi-propositional skew Boolean logic and its dual. Table1 summarises the translations between systems: the trivial translations are indicated by \? quot; and the transla- tions of interest here are denoted by \X quot;. In the table and in the sequel, S is the enriched right-handed countable-valued skew Boolean intersection algebra, Sd is the enriched left-handed dual skew Boolean intersection algebra, S is quasi-propositional skew Boolean logic, Sd is quasi- propositional dual skew Boolean logic, and L is a system of rst-order logic with equality.... ..."

### Table 1. Logical and Physical Algebra Operators.

### Table 1: Tractable classes of the point algebra for partially ordered time [5].

"... In PAGE 19: ... xky i neither x y nor y x The point algebra for partially ordered time has been throughly investigated earlier and a total classi cation with respect to tractability has been given in Broxvall and Jonsson [4]. In Broxvall and Jonsson [5] the sets of relations in Table1 are de ned and it is proven that ?A _ A, ?B _ B, ?C _ C and D are the unique maximal tractable disjunctive classes of relations for partially ordered time. The proofs of tractability for those sets relied on a series of handmade independence proofs.... ..."

### Table 1. Tractable classes of the point algebra for partially ordered time.

2000

Cited by 2

### Table 1. The correspondence between propositional logic and algebraic inequalities.

Cited by 1

### TABLE II Four Valued Logic Algebra Used for Merge Operation

### Table 1: The axioms for boolean algebras.

1999

"... In PAGE 8: ... 3. Data speci cations In the theory pCRL, the data must be given by means of a many-sorted equational speci cation D = h ; Ei that contains the axioms of boolean algebra (see Table1 ); such an equational speci cation is called a data speci cation. For easier explanation of our ideas we shall focuss on a certain kind of data speci cations that have a nice correspondence with theories of rst-order predicate logic.... In PAGE 8: ... We shall occasionally refer to the function declarations of the rst kind as relations, and to those of the second kind as functions. Let us x a data speci cation D = h ; Ei of this kind; we denote by Eb the set of axioms of sort b (it contains the axioms in Table1 ), and by Ed the set of axioms of sort d. We may regard as the rst-order language that has the relations of as relation symbols and the functions of as operation symbols.... ..."