Philosophy 3349 |
Modal Logic (the logic of possibility and necessity; add sentential operators for 'it is necessary that' and 'it is possible that', where the latter can be defined as 'it is not necessary that it is not the case that'. Main interest, perhaps, is philosophical; good framework for considering a variety of issues in metaphysics. One example of many: it has been suggested that Anselm's argument for God's existence is best understood as a modal argument about necessary existence. Another example: Kripke has argued for dualism by arguing that all identities are necessary; it's not necessary that the mind is identical with some aspect of the body; so they can't be identical at all.)
Deontic Logic (logic of obligation: add sentential operators for 'it is obligatory that' and 'it is permissible that', where permissibility can be defined as 'not obligatory that not:' Again the main interest may be philosophical, in ethics. But also of interest for AI work on intelligent agents, entities that must act as well as reason, since it can be interpreted as concerned with what we ought to do in a broader sense than the moral one.)
Temporal Logic the logic of, um, time; relevant to such philosophical issues as fatalism, free will, different conceptions of time
Conditional Logic David Lewis has used his semantics for counterfactual conditionals to address a wide variety of problems, including the definition of causality and the issue of time's arrow (i.e why is it that time is "directional" given that the fundamental laws of nature are time-invariant).
Fuzzy Logic (change the semantics: instead of two truth values, T and F, let sentences take fuzzy truth values consisting of any real number between 0 and 1. Fuzzy logic is interesting, but what's even more interesting is fuzzy set theory, where set membership is fuzzy rather than yes-or-no. Has been held to have great importance for AI.)
Intuitionistic Logic (basically, logic without the rule of negation elimination. What's interesting are the philosophical motivations for this change, and ways of constructing a semantics for intuitionistic logic, since truth-tables and the like will no longer work. The philosophical motivations are in part Kantian and "constructivist," stemming from a conception of mathematical truth on which mathematical truths are more created than discovered. Kripke has an interesting semantics for intuitionistic logic.)
Paraconsistent Logic (logics that allow contradictions, sentences of the form P & ~P, to be true. Interesting for AI applications, e.g. expert systems or models of belief revision. In classical logic, from a contradiction you can derive anything. Clearly we don't want expert systems which, if they have inconsistent items in their knowledge bases, proceed to conclude that the answer to every query is "yes." Also potentially interesting with respect to paradoxes. For instance, we may be able to keep the intuitively attractive axioms of naive set theory and simply accept that consequence that there are sets that both are and are not members of themselves.)
Relevance Logic (related to the above. Don't allow just anything to follow from a contradiction; insist that the consequences must be "relevant" to the contradiction. Also aims to avoid other "paradoxes of implication.")
Many-Valued Logic (allow additional truth values, e.g. neither true nor false. Why? One reason: idea that sentences about the future are not (now) true or false. Another reason: idea that sentences with false presuppositions are neither true nor false. Example: "True or false: you have stopped beating your spouse." If you never started beating your spouse, neither 'true' nor 'false' seems like the right answer.)
Nonmonotonic Logic (A logic is monotonic if adding premises to an argument cannot invalidate the argument. If we want logic to give us an account of rational belief revision, it seems that it will need to be nonmonotonic. One way to put this is that inferences are defeasible: after gathering further evidence, we may want to withdraw a conclusion we drew earlier.)
Free Logic (allows names that don't refer to anything and models with an empty universe)
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Last update: February 7, 2002 |