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Modal logic In languages, modality deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles.

For example, "We go to the games" can be modified to give "We should go to the games", and "We can go to the games" and perhaps "We will go to the games". More abstractly, we might say that modality affects the circumstances in which we take an assertion to be satisfied.

Confusing modality is known as the modal fallacy. Aristotle 's logic is in large parts concerned with the theory of non-modalized logic.

His work unleashed a torrent of new work on the topic, expanding the kinds of modality treated to include deontic logic and epistemic logic. The seminal work of Arthur Prior applied the same formal language to treat temporal logic and paved the way for the marriage of the two subjects.

Saul Kripke discovered contemporaneously with rivals his theory of frame semanticswhich revolutionized the formal technology available to modal logicians and gave a new graph-theoretic way of looking at modality that has driven many applications in computational linguistics and computer sciencesuch as dynamic logic.

Informal reasoning and dialectic[ edit ] Main articles: Informal logic and Logic and dialectic The motivation for the study of logic in ancient times was clear: Half of the works of Aristotle's Organon treat inference as it occurs in an informal setting, side by side with the development of the syllogistic, and in the Aristotelian school, these informal works on logic were seen as complementary to Aristotle's treatment of rhetoric.

This ancient motivation is still alive, although it no longer takes centre stage in the picture of logic; typically dialectical logic forms the heart of a course in critical thinkinga compulsory course at many universities. Dialectic has been linked to logic since ancient times, but it has not been until recent decades that European and American logicians have attempted to provide mathematical foundations for logic and dialectic by formalising dialectical logic.

Dialectical logic is also the name given to the special treatment of dialectic in Hegelian and Marxist thought. There have been pre-formal treatises on argument and dialectic, from authors such as Stephen Toulmin The Uses of ArgumentNicholas Rescher Dialectics[32] [33] [34] and van Eemeren and Grootendorst Pragma-dialectics.

Theories of defeasible reasoning can provide a foundation for the formalisation of dialectical logic and dialectic itself can be formalised as moves in a game, where an advocate for the truth of a proposition and an opponent argue. Such games can provide a formal game semantics for many logics.

Argumentation theory is the study and research of informal logic, fallacies, and critical questions as they relate to every day and practical situations. Specific types of dialogue can be analyzed and questioned to reveal premises, conclusions, and fallacies. Argumentation theory is now applied in artificial intelligence and law.

Mathematical logic Mathematical logic comprises two distinct areas of research: Mathematical theories were supposed to be logical tautologiesand the programme was to show this by means of a reduction of mathematics to logic.

If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject. Recursion theory captures the idea of computation in logical and arithmetic terms; its most classical achievements are the undecidability of the Entscheidungsproblem by Alan Turingand his presentation of the Churchâ€”Turing thesis.

Philosophical logic Philosophical logic deals with formal descriptions of ordinary, non-specialist "natural" languagethat is strictly only about the arguments within philosophy's other branches.

Most philosophers assume that the bulk of everyday reasoning can be captured in logic if a method or methods to translate ordinary language into that logic can be found.

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Philosophical logic is essentially a continuation of the traditional discipline called "logic" before the invention of mathematical logic. Philosophical logic has a much greater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a great deal to the development of non-standard logics e.

Kripke 's supervaluationism in the semantics of logic. Logic and the philosophy of language are closely related. Philosophy of language has to do with the study of how our language engages and interacts with our thinking. Logic has an immediate impact on other areas of study.The college essays are often printed in various colors of ink.

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