Semantics of wffs Given an interpretation l=< D, lo> and an assignment o, I(o (A), the value of A with respect to o in l. for each wff is defined as follows I(p(o)=lo(p)if p is a propositional constant I(p)o=o(p) if p is a propositional variable T(Pt1…tn)(σ)=o(P")(t1)()…T(tn)(a) if Pn is an n-ary predicate constant, and t1,…, tn are terms T(P"t1…tn)(σ)=σ(P")(t1)(σ)…(tn)(σ if Pn is an n-ary predicate variable, and ,……, t are terms. Logic in Computer Science -p 6/18Semantics of Wffs Given an interpretation I =< D, I0 > and an assignment σ, I(σ)(A), the value of A with respect to σ in I, for each wff, is defined as follows • I(p)(σ) = I0(p) if p is a propositional constant. • I(p)(σ) = σ(p) if p is a propositional variable. • I(Pnt1 · · ·tn)(σ) = I0(Pn)I(t1)(σ)· · · I(tn)(σ) if Pn is an n-ary predicate constant, and t1, · · · ,tn are terms. • I(Pnt1 · · ·tn)(σ) = σ(Pn)I(t1)(σ)· · · I(tn)(σ) if Pn is an n-ary predicate variable, and t1, · · · ,tn are terms. Logic in Computer Science – p.6/18