{"id":302,"date":"2017-05-07T22:25:12","date_gmt":"2017-05-07T12:25:12","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/?p=302"},"modified":"2017-05-07T22:44:28","modified_gmt":"2017-05-07T12:44:28","slug":"t-legality-a-modality-for-legal-activists","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2017\/05\/07\/t-legality-a-modality-for-legal-activists\/","title":{"rendered":"T-Legality &#8211; A Modality for Legal Activists"},"content":{"rendered":"<p><span style=\"color: #000000;\">From <a href=\"https:\/\/www.theatlantic.com\/business\/archive\/2008\/05\/obama-will-stop-the-mean-corporations-from-stealing-all-our-jobs\/3396\/\">Megan McArdle<\/a><\/span><\/p>\n<p><span style=\"color: #000000;\">A commenter claims:<\/span><\/p>\n<p><span style=\"color: #000000;\">Umm, you can make &#8220;corporations&#8221; (or engineers) give us more fuel-efficient cars simply by increasing fuel efficiency standards. If they passed a law tomorrow that said all cars sold by 2010 must get 45mpg, Detroit could do that pretty easily. They just don&#8217;t, because they don&#8217;t have to.<\/span><\/p>\n<p><span style=\"color: #000000;\">Apparently making a law that P means that P is the case. It\u2019s an interesting point of view. Let\u2019s see if we can establish a modal logic for that view of legislative power.<\/span><\/p>\n<p><span style=\"color: #000000;\">We define the modal operators <strong>L<\/strong> (the analogue to []) and <strong>P<\/strong> (like &lt;&gt;)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>L<\/strong>p =: It\u2019s a law that p<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>P<\/strong>p =: ~<strong>L<\/strong>~p =: it\u2019s legal that p<\/span><\/p>\n<p><span style=\"color: #000000;\">Let\u2019s take the semantic approach by defining the rules of the semantic tableaux for the appropriate logic.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LN<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ~<strong>P<\/strong>X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\/<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>L<\/strong>~X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ~<strong>L<\/strong>X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\/<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>P<\/strong>~X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\"><strong>PR<\/strong>\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>P<\/strong>X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\/<em>v<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<em>w<\/em>A<em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 where <em>v<\/em> is new to this path<\/span><\/p>\n<p><span style=\"color: #000000;\">The accessibility relation A is a legal accessibility relation, and the indexes on the right indicate legal worlds.\u00a0<strong>PR<\/strong> tells us that if X is not forbidden by law in w then in some state v, accessible by lawyers from <em>w<\/em> X occurs.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LR<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>L<\/strong>X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\\<em>v<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<em>w<\/em>A<em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">Which tells us that if X is mandated by law in <em>w<\/em>, then in any state <em>v<\/em> accessible by lawyers from <em>w<\/em> X occurs.<\/span><\/p>\n<p><span style=\"color: #000000;\">We know that <strong>L<\/strong>A -&gt; A, which is a statement of Legal Reflexivity, won\u2019t be a valid formula in this logic (try the tree and see,) but if we add the rule (following the Hintikka strategy:)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LT<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>L<\/strong>X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">Or if we declare that the accessibility relation is reflexive (according to the Orthodox strategy:)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Refl<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>A<em>w<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for any <em>w<\/em> on this branch<\/span><\/p>\n<p><span style=\"color: #000000;\">We also know that there is an axiomatization that will give us just the same valid formulas in <strong>LTS<\/strong>:<\/span><\/p>\n<p><span style=\"color: #000000;\">We need a rule of inference of Legal Necessitation on the analogy of plain Necessitation:<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LR1<\/strong>:\u00a0|- A =&gt;\u00a0|- <strong>L<\/strong>A<\/span><\/p>\n<p><span style=\"color: #000000;\">Which, curiously enough, indicates that anything that can be shown to be a thesis in the logic must be a Law.<\/span><\/p>\n<p><span style=\"color: #000000;\">The axioms required are<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>L1:\u00a0<\/strong> <strong>L<\/strong>(A -&gt; B) -&gt;\u00a0(<strong>L<\/strong>A -&gt;\u00a0LB)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (Distribution of <strong>L<\/strong> over -&gt;\u00a0)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>L2:<\/strong> <strong>L<\/strong>A -&gt;\u00a0A \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Reflexivity)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>L1<\/strong> itself would give us <strong>KL<\/strong> (Lawyers\u2019 <strong>K<\/strong>,) and it has the at first sight odd result of saying that if it is a law that A -&gt;\u00a0B then if it\u2019s a law that A, it is equally a law that B. But how odd is that? We could reasonably understand this as a statement of proper legal interpretation: if the law states that A and the law also states that whenever A then B, then it is at least implicitly according to law that B. (Roe vs. Wade seems to have been decided in this way.)<\/span><\/p>\n<p><span style=\"color: #000000;\">The axiom <strong>L2<\/strong> gives us <strong>TL<\/strong>, Lawyers\u2019 <strong>T<\/strong>. It\u2019s an explicit statement of the claim that we started with.<\/span><\/p>\n<p><span style=\"color: #000000;\">This is a fairly weak logic, even amongst Normal logics. Do we want to add any other conditions? Do we want to give the legal accessibility relation symmetry or transitivity? What would these look like?<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LT<\/strong> to <strong>L4<\/strong>?\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">Add the property of transitivity to the accessibility relation in <strong>LT<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Trans<\/strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<em>w<\/em>A<em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<em>v<\/em>A<em>u<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>w<\/em>A<em>u<\/em><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\">Try\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>L<\/strong>p -&gt; <strong>LL<\/strong>p<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 We find that it closes in <strong>L4<\/strong> but not in <strong>LT<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\">Is this something we want? That if it\u2019s a law that X then it\u2019s a law that it\u2019s a law that X? That actually seems quite reasonable, especially if we interpret \u2018being a law\u2019 in the way that we did for the distributivity axiom. Thus; if it\u2019s a law that X then it\u2019s at least implicitly according to law that it\u2019s a law that X. Perhaps this is referring to some sort of constitutional understanding of the law.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LT<\/strong> to <strong>LB<\/strong>?<\/span><\/p>\n<p><span style=\"color: #000000;\">Add the property of symmetry to the accessibility relation in <strong>LT<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Sym\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><em>w<\/em>A<em>v<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &#8230;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>v<\/em>A<em>w<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">Try\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 p -&gt; <strong>LP<\/strong>p<\/span><\/p>\n<p><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 We find that it closes in <strong>LB<\/strong> but not in <strong>LT<\/strong>.<\/span><\/p>\n<p><span style=\"color: #000000;\">Is this something we want? It\u2019s a bit harder to understand. If something is occurring then by law there is no law against it. I have to say, that seems unlikely. So let\u2019s not go so far as <strong>LB<\/strong>. (Nor, of course, can we accept <strong>L5<\/strong>, which we\u2019d get by making the relation an equivalence relation.) So the accessibility relation can\u2019t be symmetric: if <em>v<\/em> is accessible to lawyers from <em>w<\/em> it doesn\u2019t follow that <em>w<\/em> is accessible to lawyers from <em>v<\/em>.<\/span><\/p>\n<p><span style=\"color: #000000;\">Even if we just stick to <strong>LT<\/strong> there are plenty of interesting results for the lawyers to get busy on. The following are all provable in <strong>LTS<\/strong>:<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS1:\u00a0\u00a0\u00a0\u00a0L<\/strong>(A &lt;-&gt; B) -&gt;\u00a0(<strong>L<\/strong>A &lt;-&gt;\u00a0<strong>L<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS2:\u00a0\u00a0\u00a0\u00a0L<\/strong>(A &amp; B) &lt;-&gt;\u00a0(<strong>L<\/strong>A &amp; <strong>L<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS3:\u00a0\u00a0\u00a0\u00a0L<\/strong>A &lt;-&gt;\u00a0~<strong>P<\/strong>~A<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS4:\u00a0\u00a0\u00a0\u00a0L<\/strong>~A &lt;-&gt;\u00a0~<strong>P<\/strong>A<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS5:\u00a0\u00a0\u00a0\u00a0<\/strong>~<strong>P<\/strong>(A v B) &lt;-&gt;\u00a0(~<strong>P<\/strong>A &amp; ~<strong>P<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS6:<\/strong>\u00a0\u00a0\u00a0\u00a0<strong>P<\/strong>(A v B) &lt;-&gt;\u00a0(<strong>P<\/strong>A &amp; <strong>P<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS7:\u00a0\u00a0\u00a0<\/strong>\u00a0<strong>L<\/strong>(A -&gt;\u00a0B) -&gt;\u00a0(<strong>P<\/strong>A -&gt;\u00a0<strong>P<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS8:\u00a0<\/strong>\u00a0\u00a0\u00a0(<strong>L<\/strong>A v <strong>L<\/strong>B) -&gt;\u00a0<strong>L<\/strong>(A v B)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>LTS9:\u00a0\u00a0\u00a0\u00a0P<\/strong>(A &amp; B) -&gt;\u00a0(<strong>P<\/strong>A &amp; <strong>P<\/strong>B)<\/span><\/p>\n<p><span style=\"color: #000000;\">Actually, I started writing this as a bit of a joke, but I now wonder if there might not be a non-silly way to apply modality to laws.\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>From Megan McArdle A commenter claims: Umm, you can make &#8220;corporations&#8221; (or engineers) give us more fuel-efficient cars simply by increasing fuel efficiency standards. If they passed a law tomorrow that said all cars sold by 2010 must get 45mpg, Detroit could do that pretty easily. They just don&#8217;t, because they don&#8217;t have to. Apparently [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-302","post","type-post","status-publish","format-standard","hentry","category-philosophy"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/302","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/comments?post=302"}],"version-history":[{"count":3,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/302\/revisions"}],"predecessor-version":[{"id":305,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/302\/revisions\/305"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}