We define propositional functions H (h,t,s), T(h,t,s) and S(h,t,s) on

propositional variable h, t and s that provide ethics compliant values for h, t and s to ensure that the knife performs its functions in agreement with ethical theory A.

It assigns each

propositional variable P an arbitrary subset [parallel]P[parallel] [subset or equal to] X and satisfies the following conditions for every F, G [member of] [L.sub.[??]]:

(a) the equation a==0 is denoted by a

propositional variable a#0, and the inequation a!=0 is denoted by a literal [logical not]a#0;

Aristotle's Thesis is a negated conditional, which consists of one

propositional variable with a negation either in the antecedent (version 1) or in the consequent (version 2).

In this paper we focus on the intuitionistic propositional logic with one

propositional variable. More precisely we consider the standard fragment {[right arrow], [disjunction], [perpendicular to]} of this logic and compute the proportion of tautologies among all formulas.

The basic idea of this encoding is that each term can be represented uniquely by a valuation of a set of

propositional variables, such that for each fluent f the

propositional variable [Z.sub.f] is true iff f occurs in the term.

Then S' = ??([Gamma], [Delta] + A) and S" = ??([Lambda] + A, [Pi]) are both smaller than ??([Gamma] + [Lambda], [Delta] + [Pi]), and A is a

propositional variable in S.

where "x" is a first-order variable and "P" is a

propositional variable that has the same range as "x".(12) "True" functions syntactically as a predicate, and the above definition would confer upon it a genuine semantic role.

For example, given T the theory of Equality with Uninterpreted Functions, if p is a

propositional variable, then p, x = f(y) are T-atoms and p, [logical not]p, x = f(y) and x [not equal to] f(y) are T-literals.

For example, in the context of the dinner-date problem described previously, the

propositional variable [garb.sub.0] means that there is garbage in the initial state, ??[garb.sub.2] signifies that there is no garbage after executing the first set of parallel actions, and [carry.sub.1] means that the carry action is executed at time one.