# System Kt (K sub t)

## Notes

This system is E.J. Lemon's Kt system.

It was designed to be a minimal tense logic.

The terms are

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

## Based on

With G and H undefined it is:

• System PC
• Definitions
• Fa = NGNa
• Pa = NHNa
• Rules
• If |- a, infer |- Ga
• If |- a, infer |- Ha
• Axioms
• G(p>q)>(Gp>Gq)
• H(p>q)>(Hp>Hq)
• PGp>p
• FHp>p

[Prior, 1967, p176]

### OR

With F and P undefined.

• System PC
• Definitions
• Ga = NFNa
• Ha = NPNa
• Rules
• If |- a, infer |- Ga
• If |- a, infer |- Ha
• Axioms
• G(p>q)>(Fp>Fq)
• H(p>q)>(Pp>Pq)
• PGp>p
• FHp>p

[Prior, 1967, p176]

## Basis for

Kt plus the definition [ La == a & Ga ] Gives von Wright's system M. [Rescher and Urquhart, 1971, p126] (Which is T (Feys) [Hughes and Cresswell, 1968, p125]

Kt plus the definition [ La == a & Ga & Ha ] gives system B (The Brouwerian system) [Rescher and Urquhart, 1971, p127]

Kb is formed by Kt plus the axioms:

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

[Rescher and Urquhart, 1971, p76]