System K_b (K sub b)

[Rescher and Urquhart, 1971]

Notes

In some sense, K_b is K_t with branching time restrictions.

The terms are inherited from K_t

• G: It will always be
• H: It has always been
• P: Past
• F: Future

Based on

K_b is any of the bases for K_t plus the axioms of:

• G3: Gp>GGp
• H3: Hp>HHp
• H4: (H(p+q)&H(p+Hq)&H(Hp+q))>(Hp+Hq)

[Rescher and Urquhart, 1971, p76]

Basis for

K_L is K_b plus the axiom G4: (G(p+q)&G(p+Gq)&G(Gp+q))>(Gp+Gq)

[Rescher and Urquhart, 1971, p90]

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