abstract. We survey a number of decidablity and undecidablity results concerning epistemic temporal logic. The goal is to provide a general picture which will facilitate the ‘sharing of ideas ’ from a number of different areas concerned with modeling agents in interactive social situations. 1

Abstract. In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin ” operator, then the resulting “semijoin algebra ” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to µGF. 1.

s 0 t 0 there is a t 2 W such that Rst and tZt 0 . If there is some bisimulation Z linking s and s 0 then we say that s and s 0 are bisimilar, notation: s $ s 0 , or M; s $ M 0 ; s 0 if we wish to make the models explicit. Figure 1 contains two simple examples of bisimulating models (the models bisimulate horizontally) in a language with only one unary relation P . Figure 2 shows two models which do not bisimulate at the roots; all states in both models satisfy the same unary relations; M 0 has all of the nite branches that M has, but in addition it contains an innite branch. p p s w 0 s<F11.

This paper gives motivations, de nitions and some initial results

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