### Table 1. The Vector semiring

2005

Cited by 3

### Table 2 The Vector semiring

### Table 1. The family of (max; +) and tropical semirings :::

"... In PAGE 4: ... Essentially all the standard notions of algebra have obvious semiring analogues, provided they do not appeal to the invertibility of addition. There are several useful variants of the (max; +) semiring, displayed in Table1 . In the sequel, we will have to consider various semirings, and will universally use the notation ; ; 0; 1 with a context dependent meaning (e.... ..."

### Table1. Relationships between semiring elements.

"... In PAGE 6: ... Definition 2 (semiring). The class of semirings is denoted by CB and is defined as CB BMBMBP CBBD CY A1 A1 A1 CY CBD2 CY CB A2 CB By using the properties of A2, B7 and of the cartesian product, we can write down some basic relationships between semiring elements; In Table1 symbol BR denotes any of the semiring operator A2 and B7. The table shows how the semiring operations of the cartesian product is defined using the corresponding operations in the primitive semiring.... ..."

### Table1. Relationships between semiring elements.

"... In PAGE 6: ... Definition 2 (semiring). The class of semirings is denoted by CB and is defined as CB BMBMBP CBBD CY A1 A1 A1 CY CBD2 CY CB A2 CB By using the properties of A2, B7 and of the cartesian product, we can write down some basic relationships between semiring elements; In Table1 symbol BR denotes any of the semiring operator A2 and B7. The table shows how the semiring operations of the cartesian product is defined using the corresponding operations in the primitive semiring.... ..."

### Table 1. Semirings for validity, recency, and trust.

2003

"... In PAGE 5: ... Intuitively, Tr(c) denotes the confidence that the issuer of c has in the relationship expressed by the certificate c. The trust level of a certificate chain ck ck 1 c1 is Nk i=1 Tr(ci), where N is defined in Table1 . Suppose that Alice wants to use server S, but S requires a certificate chain that has a trust level above a certain value v.... ..."

Cited by 12

### TABLE 1. The family of (max, +) and tropical semirings . . .

1998

Cited by 1

### Table 3. Provenance queries

2007

"... In PAGE 18: ...2 Provenance queries A wide range of scientiflc queries can be answered based on our provenance on- tology model enhanced with reasoning capabilities. In Table3 , we present several such queries that our e-scientist collaborators are interested in. For each query expressed in English, we construct a SPARQL query and its SQL counterpart using our translation algorithms.... ..."

Cited by 1