### Table 1: (Un)decidability of the equational theories of classes of cylindric algebras.

1999

"... In PAGE 6: ... In fact, the expansion Crs+ 3 of Crs3 with a single operation k1 1 has an undecidable equational theory. We summarized these results in Table1 . We note that, similarly to the relation algebra case, the unde- cidable equational theories are in fact r.... ..."

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### 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.... ..."

### Table 2: (Un)decidability of some subvarieties of RL

2002

"... In PAGE 33: ... Since modular lattices have an undecidable equational theory ([Fr80]), the same is true for modular residuated lattices. Table2 summarizes what is currently known about the decidability of various sub-... ..."

### Table 3: The axioms for boolean algebras.

1998

"... In PAGE 9: ... n28We have kept our numbering consistent with Groote and Ponse n281994an29; in their setting Sum2 den0cnes n0b-conversion.n29 Let n06 be a pCRL-signature, then the pCRL-theory n05 n06 for n06 consists of the axioms depicted in Table 2 and the axioms for boolean algebras depicted in Table3 . A n06-algebra A is called a pCRL-algebra if A j=n05 n06... ..."

### Table 3: Operations in 3-valued boolean algebra

### Table 2. Some constraints expressible as interior algebra equations.

1998

"... In PAGE 6: ...eaning as operators on sets. X is the complement of X w.r.t. U (i.e. X = U ?X). Interior algebraic equations provide a constraint language for describing topolog- ical relationships between sets of points in a topological space. Some of the more signi cant constraints which can be expressed are given in Table2 . Reasoning with such equations is far more practicable than reasoning in a set-theoretic language based on the `2 apos; relation.... ..."

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### Table 2: Some signi cant relations de nable within the RCC theory. This means we do not have a full Boolean algebra of regions; but, in order that appropriate regions exist to ful l the requirements of the quasi-Boolean structure suggested by the above de nitions, the basic RCC theory is supplemented with the following existential axioms:2 RCC4) 9x8y[C(x; y)]

"... In PAGE 4: ... The relation C(x; y) is re exive and symmetric, which is ensured by the following two axioms: RCC1) 8xC(x; x) RCC2) 8xy[C(x; y) ! C(y; x)] We also require C to be extensional:1 RCC3) 8xy[8z[C(z; x) $ C(z; y)] ! x = y] Using C(x; y) a very large class of intuitively signi cant relations can be de ned. Some of the most useful of these are illustrated in Figure 1 and their de nitions are given in Table2 . The non-symmetrical relations P, PP, TPP and NTPP have inverses which we write as Ri, where R 2 fP; PP; TPP; NTPPg.... ..."

### Table 6: Some equations for the streams generated by M

"... In PAGE 12: ... Algebra of boolean streams Third, we take the subalgebra of the boolean stream algebra generated by the Thue-Morse sequence M. Some of the extra equations that hold in this algebra are in Table6 . The equations for the difference streams give in fact recurrence equations for these streams, which were observed empirically from Table 7.... ..."

### Table 1 Aspects of Boolean Map Theory

2007

"... In PAGE 8: ...6 Boolean Map Theory Compared With Previous Theories Many components of Boolean map theory resemble elements in previous theories. Table1 lists some of the claims and other unique aspects in Boolean map theory and refers to some of the theories that these claims agree with or challenge. This table should help to place the present framework in the context of the literature.... ..."

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### Table 8: Some common Geometric Algebra operations.

2004

"... In PAGE 42: ... The large number of basic operations. Table8 lists some basic operations that every GA implementation should provide. 3.... ..."

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