### Table 1. Logics for belief fusion

"... In PAGE 9: ... Therefore, the results in this paper fill a gap in the previous work. We believe that the logics, which are summarized in Table1 , are applicable to reasoning in multi-agent... ..."

### Table 2. Summary of probabilistic beliefs and correct forecasts Variable

"... In PAGE 8: ... Statistical summary for these probabilistic beliefs vis. correctness of the respective forecasts on a firm-by-firm basis are summarized in Table2 for all periods (deviations across periods, as well as across industries and regions, were most often statistically in- significant for all reported indicators). The upper part of the table reports the main summary statistics; it clearly implies that the managers were quite confi- dent in their forecasts: the average probabilistic belief varied across indicators from 74.... ..."

### Table 1 summarizes the relations between the complexity classes, probabilistic satis ability prob- lems, belief network problems, and planning prob- lems discussed.

1999

"... In PAGE 4: ...satis ability problem Boolean formula belief network problem planning problem NP Sat 9x1; : : : ; 9xn(E[ (x)] ) most probable explanation best trajectory PP Majsat Rx1; : : : ; R xn(E[ (x)] ) belief updating (inference) plan evaluation NPPP E-Majsat 9x1; : : : ; 9xc; R xc+1; : : : ; R xn(E[ (x)] ) maximum a posteriori hypothesis best polynomial size plan PSPACE SSat 9x1; R x2; : : : ; 9xn?1; Rxn(E[ (x)] ) in uence diagrams best polynomial horizon plan Table1 : Di erent arrangements of quanti ers result in P-Sat problems complete for di erent complexity classes and correspond to basic problems in uncertain reasoning and planning. here, but the reduction essentially consists of creat- ing one variable per node in the belief network and one per conditional probability table entry.... ..."

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### Table 1: A collection of probabilistic-logical models together with their underlying probabilistic and logical formalism.

"... In PAGE 1: ... Each subarea focuses on its own language con- cepts. Consider Table1 which lists a subset of proposed for- malisms 1. The language concepts vary from acyclic to cyclic models, from logically structured dependencies among ran- dom variables to states, from finite to continuous random variables, and from functor-free languages to Prolog.... ..."

### Table 1. A system is said to be purely probabilistic if its behaviour can be completely speci ed by a probabilistic distribution. A system is called a generalized probabilistic system if it exhibits both a probabilistic behaviour and a nondeterministic behaviour. (These terms are de ned in the next section.) S stands for the size of a system, and F for the size of a formula.

"... In PAGE 18: ... Table1 : Time complexities of model checking procedures in probabilistic logics. S denotes the size of the system being veri ed and F stands for the size of a formula that specify a probabilistic temporal property.... ..."

### TABLEAUX apos;95, volume 918 of LNAI, pages 79{94. Springer-Verlag, 1995. 19. J. Y. Halpern and Y. Moses. A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief. Arti cial Intelligence, 54:319{379, 1992. 20. D. Harel, A. Pnueli, and J. Stavi. Propositional Dynamic Logic of Nonregular Programs. Journal of Computer and System Sciences, 26:222{243, 1983. 21. J. E. Hopcroft and J. D. Ullman. Introduction to automata theory, languages, and computation. Addison-Wesley Publishing Company, 1979. 22. G. E. Hughes and M. J. Cresswell. A Companion to Modal Logic. Meuthuen, 1984. 23. G. E. Hughes and M. J. Cresswell. A New Introduciton to Modal Logic. Routledge, 1996.

1998

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### Table 2: BAT Results with Manually Optimized Ordering

2002

"... In PAGE 9: ... After enough effort, we were able to find a good ordering that allows symbolic simulation to run. Table2 shows the results. In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion.... In PAGE 9: ... In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion. By comparing the results in Table 1 and in Table2 , we observe that variable ordering sig- nificantly impacts the performance of symbolic simulation. For the OBDD sizes, we show two types of data: the total number of OBDD nodes at the end of symbolic simulation (to- tal OBDD nodes), and the maximum number of OBDD nodes during the symbolic simulation (max OBDD nodes).... ..."

Cited by 1