### Table 4 Additional Axioms for Core XPath

"... In PAGE 6: ...inite trees in [3]. We will skip over most of the details, see [5] for more information. The new group of axioms we add are tree axioms, analogous to those used in [3]. They are given in Table4 . TreeAx1 is a Kleene algebra axiom [13,14], well-known to anyone familiar with PDL, denoted as Mix in [9].... ..."

### Table 1: Axioms of ACP(A; ) and additional ones of ACP (A; ), a; b 2 A [ f ; g, H; I A. BKS axioms for binary Kleene star.

"... In PAGE 7: ... ACP(A; ) is further extended to ACP (A; ) (ACP with branching bisimulation) by adding the constant (silent step) and hiding I (renaming actions in I A into ). Process ex- pressions are subject to the axioms of ACP (A; ), displayed in Table1 (x; y; z; ::: ranging over processes). Note that + and are associative, and that + also is commutative and idempotent.... In PAGE 7: ... For a detailed introduction to ACP(A; ), ACP (A; ) and SC we refer to [BW90]. Axioms for the -operation are included in Table1 . In [FZ94], Fokkink and Zantema prove that (A1){(A5) and (BKS1){(BKS3) axiomatize strong bisimilarity for processes de ned with +; and .... In PAGE 18: ...e., Basic Process Algebra de ned by axioms (A1){(A5) of ACP(A; ) (see Table1 ) together with x$ y = x(x$ y)(x$ y) + y and RSP$ is complete with respect to strong bisimilarity over that signature. Transition rules for $ are x a ??! p x$ y a ??! (x$ y)(x$ y) y$ x a ??! p x a ??! x0 x$ y a ??! x0(x$ y)(x$ y) y$ x a ??! x0 and the remaining transition rules and strong bisimulation equivalence are de ned as usual (cf.... ..."

### Table IV. Transition rules for the binary Kleene star

2004

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### Table 6: Kleene three-valued connectives

2004

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### Table 6: Kleene three-valued connectives

2004

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### Table IV. Transition rules for the binary Kleene star

### Table 3: Axioms and SOS rules for the binary Kleene star

1995

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### Table 3: Axioms and SOS rules for the binary Kleene star

1995

Cited by 2