Intensional Predicate Logic with Anaphora

Intensional model
w1w2w3w4
1, 2, 3 1, 2, 3 1, 2, 3 1, 2, 3
[], w1
[], w2
[], w3
[], w4

Predicates (all one place): number, odd, even, prime, composite, red, green, large, small

(The number properties are the expected necessary truths, and the color and size properties are as displayed.)

Formulae
predn(arg1,...,argn)atomic
(c = c')equality
~Anegation
(A & B)conjunction
(A | B)disjunction
EX Aexistential
<>Amodal
+pred(arg)additive particle
(A - B)apposition
  • Equality statements have parentheses. pred(arg) statements do not.
  • Pronouns are written pN, where N is any integer. They can be arguments to predicates and =.
  • Variables must be in capital letters.
  • No free variables.
  • The existential binds exactly one variable (though Es can be nested).
  • White space in formulae is ignored.
  • In appositives A - B, formula B is interpreted in the actual state (even when deeply embedded).
  • A formula +pred(arg) is defined iff pred(arg') is entailed by the input state, for arg ≠ arg'. Where defined, the update is pred(arg).