### Table 2. Sequent calculi and their conditions depending on the selected logic

1999

"... In PAGE 7: ...Table 2. Sequent calculi and their conditions depending on the selected logic Table2 uniformly describes the rules of all sequent calculi. The rules are arranged according to the tableau classi cation and directly usable for cumulative domains.... ..."

Cited by 9

### TABLEAUX apos;96, Springer LNAI 1071, pp. 127{142, 1996. [5] P. A. Bonatti. A Sequent Calculus for Skeptical Default Logic. Proceedings TABLEAUX apos;97, Springer LNAI 1227, pp. 107{121, 1997. [6] D. van Dalen. Intuitionistic Logic. Handbook of Philosophical Logic, Vol. III, pp. 225{339, 1986.

### Table 1: Complexity of model checking for default logic

1999

"... In PAGE 4: ... The above property and Theorem 6 also imply p 2- completeness of model checking for prerequisite-free dis- junctive default theories. In Table1 we summarize the complexity results de- scribed in this section. Each column of the table corre- sponds to a di erent condition on the conclusion part of default rules.... In PAGE 6: ... From the computational viewpoint, it turns out that Liberatore and Schaerf apos;s notion of model checking is harder than the one presented in this paper. In fact, comparing Table1 with the results reported in [Liber- atore and Schaerf, 1998], it can be seen that our for- mulation of model checking is computationally easier in almost all the cases examined, with the exception of nor- mal and supernormal default theories, for which the com- plexity of the two versions of model checking is the same. 6 Conclusions In this paper we have studied the complexity of model checking in several nonmonotonic logics.... ..."

Cited by 1

### Table 2. The focussed sequent calculus of permutative logic

"... In PAGE 14: ...Table2 . Its negative logical inferences are identical to those of the standard sequent calculus.... ..."

### Table 1. The sequent calculus of permutative logic.

"... In PAGE 4: ... If = f(a; b); (c); (d; e)g; 2, then its genus is given by the couple (2; 3) and rk( ) = 6. The multiplicative permutative calculus is recalled in Table1 ; moreover, the involutive duality is given by De Morgan rules: (A O B)? = B? A? ([A)? = #A? }? = h ?? = 1 (A B)? = B? O A? (#A)? = [A? h? = } 1? = ?: By the fact that basic commutations are not provable keeping the lowest topo- logical complexity, PL turns out to be an inference system able to deal with logical noncommutativity. As suggested by some of the next propositions, basic commutations can be recovered throughout the two permutative modalities [ and #.... ..."

### Table 1. Description logic ALC

1997

"... In PAGE 2: ... We use the notation of DLs, focusing on the well-known DL ALC, corresponding to the standard PDL with atomic programs only. Table1 summarizes the syntax and the semantics of ALC and the corresponding PDL. In addition, weusethetwo nonmonotonic modal operators: a minimal knowledge operator K and a default assumption operator A.... ..."

Cited by 30

### Tableaux calculi for modal predicate logics with and without the Barcan formula can be found in [32]. Just like the identity of individuals gives rise to many philosophical ques- tions in modal predicate logic, it also gives rise to many deep mathematical questions. As a result, various alternative semantic frameworks have been developed for modal predicate logic during the 1990s, including the Kripke bundles of Shehtman and Skvortsov [37] and the category-theoretic seman- tics proposed by Ghilardi [16] The notion of (axiomatic) completeness is another source of interesting mathematical questions in modal predicate logic. It turns out that the mini- mal predicate logical extension of many well-behaved and complete proposi- tional modal logics need not be complete. The main (negative) result in this area is that among the extensions of S4, propositional modal logics L whose minimal predicate logical extension is complete must have either L S5 or

### Table II. Principle mechanism for translating F-Logic to predicate logic

1999

Cited by 212

### Table 2. Principle of Translating Frame Logic to Predicate Logic

"... In PAGE 10: ... We adopted that approach: the input is processed and translated in several stages: The first step (besides the necessary parser) is the Frame-Logic-translator, that translates the Frame-Logic expressions to first-order logic expressions. Table2 gives an idea of how this translation is performed, but it does not catch the complete translation: e.g.... ..."