By Michael Fisher, Richard Owens
This quantity provides the completely revised lawsuits of the IJCAI '93 Workshop on Executable Modal and Temporal Logics held in Chambery, France in August 1993.
The direct execution of logical statements, via languages equivalent to PROLOG, has proved remarkably profitable inside of CS and AI. lately quite a few nonclassical logics were brought and a number of other executable sorts of those logics were utilized to programming.
This quantity addresses a variety of ways to executable modal and temporal logics, not just from a logical standpoint, but in addition from programming language and alertness standpoints; moreover, an introductory survey and an annotated bibliography are presented.
Read Online or Download Executable Modal and Temporal Logics: IJCAI '93 Workshop Chambery, France, August 28, 1993 Proceedings PDF
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Extra info for Executable Modal and Temporal Logics: IJCAI '93 Workshop Chambery, France, August 28, 1993 Proceedings
Example text
X , we can express t he onepar ameter group gt X = et l x of the skew-symmetric transformation 1(x) = F . 39) are identical at t = O. 40), we get 48 3. 41) Setting t equal to zero gives the identity f(x) = F · x . 41) gives etf f2x=~FetF(F. x)e-tF - ~FetF(F . x)e-tF = etF[F. (F . x)]e- t F, and setting t equal to zero gives the identity f2 (x) = F . (F . x) . 42) where F k : x is defined recursively by F I Fk : : = F· x and x x = F· (F k - I : x) . 43) is interesting because it expresses the powers of a linear operator in terms of "powers" of its defining bivector.
51) in spin(2 , 2) by the simple projection PI(B) = 12 112 , B = 0"20"1 = -12 onto the Lie algebra so(2). For x' = Xl0"1 +X20"2 E JR2, the equivalent rotation is given by y' = exp(~e0"20"dx' exp( -~e0"20"d . The above ideas can be immediately generalized to the general Lie group GL(Nn) of null cone N" and the orthogonal subgroups SO(p, q) where p+q = n. The orthogonal group SO(p, q) acts on the space JRp,q . Thus, if we wish to work in this Lie group or in the corresponding Lie algebra, we first project the null cone Nn onto JRp ,q by using the reciprocal vector basis elements, then carry out the rotation, and finally return to the null cone by using the inverse projection.
4 Representation of Points, Lines , and Planes Using ~~2 (11 a1 Line ~ m E< .. • 2] ~2 ~ y:3 ~3 /i ! 2. 4 Representation of Points, Lines, and Planes Using Motor Algebra In this section we will model points, lines, and planes in 4D space using the special algebra of the motors 9t,0,1 ' which spans in 4D the line space using a bivector basis . 28) or X = (1,0) + I(O ,x) . We can see that in this expression the real part consists of the scalar 1 and the dual part of a 3D bivector. Since we are working in the algebra 9t0 1 spanned only by bivectors and scalars, we see that this special geometric 'algebra is the most appropriate system for line modeling.