Plausible inference: A multi-valued logic for problem solving

A new logic is developed which permits continuously variable strength of belief in the truth of assertions. Four inference rules result, with formal logic as a limiting case. Quantification of belief is defined. Propagation of belief to linked assertions results from dependency-based techniques of truth maintenance so that local consistency is achieved or contradiction discovered in problem solving. Rules for combining, confirming, or disconfirming beliefs are given, and several heuristics are suggested that apply to revising already formed beliefs in the light of new evidence. The strength of belief that results in such revisions based on conflicting evidence are a highly subjective phenomenon. Certain quantification rules appear to reflect an orderliness in the subjectivity. Several examples of reasoning by plausible inference are given, including a legal example and one from robot learning. Propagation of belief takes place in directions forbidden in formal logic and this results in conclusions becoming possible for a given set of assertions that are not reachable by formal logic

Majestic Law and the Subjective Stop

Justice John Paul Stevens subscribed to a majestic conception of the Constitution. This Article articulates and defends that vision. Majestic law and legal reasoning characteristically involve frank moral reasoning, such as one finds in the Eighth Amendment\u27s evolving standards of decency test for proportionate punishment, or in Due Process formulations such as an appeal to immutable principles of justice, which inhere in the very idea of free government. Majestic law employs moral values, norms, and judgments in legal reasoning, taking them on their own terms. Majestic legal reasoning does not weigh revealed preferences for decency, for example. It asks whether the value of decency is well served.The principal antagonist to majestic law is the belief that moral values, norms, and judgments are subjective. That is, these moral commitments are thought to be irrational, arbitrary, prejudicial, mere intuitions, emotional reactions, personal instead of public, or supernatural instead of empirical. This view of moral commitments bars them from use in legal reasoning. In other words, it imposes a subjective stop. A subjective stop can be a complete bar to moral reasoning in law, but it is more often conditional. A moral value such as decency must be reduced to a descriptive form, such as a tally of state sentencing laws, before it can have any bearing on whether a punishment is cruel and unusual under the evolving standards of decency standard.The subjective stop is premised on a mistake. Moral values, norms, and judgments are indeed subjective. It does not follow, however, that these moral commitments are irrational, arbitrary, or in any way unfit for legal reasoning.The nature and status of moral commitments is the subject matter of metaethics, and the subjectivity of moral commitments is a topic of controversy in metaethics. The subjective stop rests on a primitive emotivism: the view that morality is a set of visceral, boo or hooray exclamations. This view of morality, however, has no defenders in contemporary metaethics. This Article relies on two alternative subjectivist metaethical theories to defend majestic law and condemn the subjective stop. Allan Gibbard\u27s norm-expressivism explains that, while moral commitments are expressions of emotion, we adjudicate our moral disagreements rationally. To express a moral commitment is to affirm a system of moral norms under which that commitment is rational. A moral norm or judgment is wrong if it is rational only under a system of norms that we cannot rationally accept. Simon Blackburn\u27s quasi-realism starts from the premise that morality is subjective in the most fundamental sense: it is something that human beings project onto the world. Blackburn argues that this changes nothing in what we think or how we act morally. The world onto which we project value imposes limitations on morality, and projection is subject to its own logic, which imposes further constraints. If our moral beliefs are minimally coherent and exhibit epistemic virtues, then they earn the right to be called true. The upshot of both of these theories is a view of moral commitments as subjective, and yet rational and either true or false.Under these viable subjectivist theories of metaethics, we have no need to reduce moral commitments to descriptive terms before we allow them to operate in legal reasoning. Justice Scalia\u27s insistence that the evolving standards of decency test should give way to an inquiry into historical and contemporary practices in punishment rested on a subjective stop - and was mistaken because of it. We can determine what cruel punishment is, and to frame that question in terms of decency is a meaningful and enlightening move. Due Process does not call only for a historical inquiry into past and currently prevailing legal processes in the United States; it also calls for rational inquiry into the truth about a fair and enlightened system of justice, or the concept of ordered liberty. To say a handgun is not critical to leading a life of autonomy, dignity, or political equality, might or might not be true, but it is not enough to say, with Justice Scalia, Who says? To say this is to impose a full subjective stop. More importantly, it is, as Justice Stevens argued, an abdication of responsibility that has led to the loss of majestic law

Argumentation-Based Contract Monitoring in Uncertain Domains

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Subjective Logic and Arguing with Evidence

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Real Islamic Logic

Four options for assigning a meaning to Islamic Logic are surveyed including a new proposal for an option named "Real Islamic Logic" (RIL). That approach to Islamic Logic should serve modern Islamic objectives in a way comparable to the functionality of Islamic Finance. The prospective role of RIL is analyzed from several perspectives: (i) parallel distributed systems design, (ii) reception by a community structured audience, (iii) informal logic and applied non-classical logics, and (iv) (in)tractability and artificial intelligence

The objective Bayesian conceptualisation of proof and reference class problems

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem