### Table XI. Sizes of formulae under the different encodings. The column P 103 gives the number of propositional variables in thousands, the column C 103 the number of clauses in thousands, and the column MB the size of the DIMACS encoded formulae in CNF in megabytes. The data are on the satisfiable formulae corresponding to the length of shortest existing plans under step semantics. The shortest 1-linearization plans are in many cases shorter, and the required formulae then correspondingly smaller.

2005

Cited by 5

### Table 1. Classi cation of Signed Formulae

1994

"... In PAGE 3: ... In the sequel X and Y will range over unsigned formulae, Z and Q over signed ones and p over propositional letters. Signed formulae allow us to use the uniform notation of Smullyan and Fitting that classi es signed formulae according to their signs and principal connectives, as shown in Table1 . Informally speaking, formulae with a similar semantic behaviour (see below) are classi ed accordingly.... ..."

Cited by 52

### Table 1: Formulas and their intended meaning

1999

"... In PAGE 4: ...rom particular methods of achieving them; e.g. they may be realized by particular plans. Table1 gives the formulas appearing in this paper, together with their intended meanings. The symbol apos; denotes a proposition and an action.... ..."

Cited by 15

### Table 2. Expansion rules for propositional operators.

"... In PAGE 7: ... Otherwise, a number of nodes are created and expanded in a DFS order. The next cases, the rules of which are shown in Table2 , are processed as indicated in lines 17-23, where newc(h) and newn(h) respectively represent the set of formulas to be added to CurrentNode and NewNode. In Table 2, I represents a sequence of (zero or more) current interval modalities (SCIM).... In PAGE 7: ... The next cases, the rules of which are shown in Table 2, are processed as indicated in lines 17-23, where newc(h) and newn(h) respectively represent the set of formulas to be added to CurrentNode and NewNode. In Table2 , I represents a sequence of (zero or more) current interval modalities (SCIM). If it is replaced by 0 CIMs, the main operator of h belongs to the propositional logic.... ..."

Cited by 2

### Table 1 Formula FAUST HOL Subgoals

"... In PAGE 5: ... EXPERIMENTAL RESULTS The prover embedded in HOL was first tested for its correctness by using the propositional and first-order formulae in [KaMo 64] and [Pell 86]. The runtimes of all the Pelletier examples, except those involving equality, are as shown in Table1 . In Table 1, all the runtimes are the execution time in seconds on a SUN 4/330.... ..."

### Table 2:Runtimes of Benchmark-Formulae (* indicates times taken by the breadth-first version) Formula Time

1991

"... In PAGE 10: ...The prover embedded in HOL was first tested for its correctness by using the propositional and first-order formulae in [22] and [23]. The runtimes of the more difficult Pelletier examples are found in Table2 . The ML-code has been incorporated in the public domain version of HOL, which runs on top of Common-Lisp on a SUN 4/65.... ..."

Cited by 3

### Table 27: Proof of Proposition 5.1

2002

"... In PAGE 27: ... Hence, we obtain the table. Table27 : It is known that determining whether the conjunction of two FBDD formulas fi1 and fi2 is consistent is NP-complete (Gergov amp; Meinel, 1994b) Moreover, FBDD satisfies :C. Since fi1 ^ fi2 is inconsistent iff fi1 j= :fi2, we can reduce the consistency test into an entailment test.... ..."

Cited by 59

### Table 27: Proof of Proposition 5.1

2002

"... In PAGE 27: ... Hence, we obtain the table. Table27 : It is known that determining whether the conjunction of two FBDD formulas fi1 and fi2 is consistent is NP-complete (Gergov amp; Meinel, 1994b) Moreover, FBDD satisfies :C. Since fi1 ^ fi2 is inconsistent iff fi1 j= :fi2, we can reduce the consistency test into an entailment test.... ..."

Cited by 59

### Table II. Rules for deriving cut sequents in MALLcut. Here P ranges over propositional variables, A;B range over MALL formulas, ; range over (possibly empty) disjoint unions of MALL formulas, and ; ; 0 range over (possibly empty) disjoint unions of cut pairs. Note that the amp;-rule may superimpose one or more cut pairs from its two hypotheses (if is non-empty), or may leave all cut pairs separate (if is empty).

2003

Cited by 24

### Table II. Rules for deriving cut sequents in MALLcut. Here P ranges over propositional variables, A;B range over MALL formulas, ; range over (possibly empty) disjoint unions of MALL formulas, and ; ; 0 range over (possibly empty) disjoint unions of cut pairs. Note that the amp;-rule may superimpose one or more cut pairs from its two hypotheses (if is non-empty), or may leave all cut pairs separate (if is empty).

2003

Cited by 24