Agency and Deontic Logic by John F. Horty

By John F. Horty

John Horty successfully develops deontic good judgment (the common sense of moral thoughts like legal responsibility and permission) opposed to the heritage of a proper conception of organisation. He accommodates yes components of selection concept to set out a brand new deontic account of what brokers should do less than numerous stipulations over prolonged classes of time. supplying a conceptual instead of technical emphasis, Horty's framework permits a few contemporary matters from ethical idea to be set out sincerely and mentioned from a uniform viewpoint.

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So now we have a structure (in fact an algebra) Form/ ∼, ¬, ∧, ∨, ⇒, ≡, ⊥, ⊤ . We need to ask a couple of questions. ” Fortunately, this question has a simple answer. We have the following fact. 20 The Lindenbaum algebra satisfies the axioms of Boolean algebra. Proof: We select one of the axioms of Boolean algebra and check that it is true in the Lindenbaum algebra. We hope the reader checks the remaining axioms of Boolean algebra. The one we selected is the second De Morgan law: ¬(x ∨ y) = (¬x) ∧ (¬y).

In other words, a variable x belongs to π(M ) if it is the image of a variable in M or if it is the image of a negated variable which does not belong to M . It should now be clear that π acts as a permutation of P(Var ). 22, we can transform any set M into any other N . We formalize this in the following fact. 24 If M ⊆ Var and M |= ϕ, then π(M ) |= π(ϕ). We will illustrate the technique of permutations within logic by looking at so-called symmetric formulas. We will say that a formula ϕ is symmetric if for every permutation of variables π, π(ϕ) ≡ ϕ.

The argument for ⊤ is very similar. p1 . . pn = ψi . By the definition of v ′ , If ϕ = pi for a variable pi , then ϕ ψ1 . . ψn v ′ (pi ) = v(ψi ). Now, we have: v ′ (ϕ) = v ′ (pi ) = v(ψi ) = v p p1 . . pn ψ1 . . ψn . p1 . . pn as desired. ψ1 . . ψn In the inductive step there are five cases, corresponding to connectives ¬, ∧, ∨, ⇒, and ≡. We shall discuss the case of ⇒; the other cases are similar. So let ϕ := ϕ′ ⇒ ϕ′′ . Clearly Thus v ′ (ϕ) = v ϕ (ϕ′ ⇒ ϕ′′ ) p1 . . pn ψ1 . . ψn = ϕ′ p1 .

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