Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term paraconsistent ("beside the consistent") was not coined until 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias.Priest (2002), p. 288 and §3.3. Tradeoffs Paraconsistency involves tradeoffs. In particular, abandoning the principle of explosion requires one to abandon at least one of the following two principles:See the article on the principle of explosion for more on this. Disjunction introductionDisjunctive syllogism Example One well-known system of paraconsistent logic is the simple system known as LP ("Logic of Paradox"), first proposed by the Argentinian logician Florencio González Asenjo in 1966 and later popularized by Priest and others.Priest (2002), p. 306. It must be emphasized that LP is but one of many paraconsistent logics that have been proposed.Surveys of various approaches to paraconsistent logic can be found in Bremer (2005) and Priest (2002), and a large family of paraconsistent logics is developed in detail in Carnielli, Congilio and Marcos (2007). It is presented here merely as an illustration of how a paraconsistent logic can work. Applications Paraconsistent logic has been applied as a means of managing inconsistency in numerous domains, including:Most of these are discussed in Bremer (2005) and Priest (2002). Semantics . Paraconsistent logic has been proposed as means of providing a simple and intuitive formal account of truth that does not fall prey to paradoxes such as the Liar. However, such systems must also avoid Curry's paradox, which is much more difficult as it does not essentially involve negation. Set theory and the foundations of mathematics . Epistemology and belief revision . Paraconsistent logic has been proposed as a means of reasoning with and revising inconsistent theories and belief systems. Knowledge management and artificial intelligence . Some computer scientists have utilized paraconsistent logic as a means of coping gracefully with inconsistentSee, for example, Truth maintenance systems or the articles in Bertossi et al. (2004). or contradictoryGershenson, C. (1999). Modelling emotions with multidimensional logic. In Proceedings of the 18th International Conference of the North American Fuzzy Information Processing Society (NAFIPS ’99), pp. 42–46, New York City, NY. IEEE Press. URL information. Deontic logic and metaethics . Paraconsistent logic has been proposed as a means of dealing with ethical and other normative conflicts. Software engineering . Paraconsistent logic has been proposed as a means for dealing with the pervasive inconsistencies among the documentation, use cases, and code of large software systems.Hewitt (2008b)Hewitt (2008a)Carl Hewitt. Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic Reasoning and the Actor Model. in Vol. 52 of Studies in Logic. College Publications. . 2015. Electronics design routinely uses a four-valued logic, with "hi-impedance (z)" and "don't care (x)" playing similar roles to "don't know" and "both true and false" respectively, in addition to True and False. This logic was developed independently of philosophical logics. Quantum physics Black hole physics Hawking radiation Quantum computing Spintronics Quantum entanglement Quantum coupling Uncertainty principle
Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term paraconsistent ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias.Priest (2002), p. 288 and §3.3. Tradeoffs Paraconsistency involves tradeoffs. In particular, abandoning the principle of explosion requires to abandon at least one of the following two principles:See the article on the principle of explosion for more on this. Disjunction introductionDisjunctive syllogism Example One well-known system of paraconsistent logic is the system known as LP ("Logic of Paradox"), first proposed by the Argentinian logician Florencio González Asenjo in 1966 and later popularized by Priest and others.Priest (2002), p. 306. LP is only one of many paraconsistent logics that have been proposed.Surveys of various approaches to paraconsistent logic can be found in Bremer (2005) and Priest (2002), and a large family of paraconsistent logics is developed in detail in Carnielli, Congilio and Marcos (2007). It is presented here merely as an illustration of how a paraconsistent logic can work. Applications Paraconsistent logic has been applied as a means of managing inconsistency in numerous domains, including:Most of these are discussed in Bremer (2005) and Priest (2002). Semantics : Paraconsistent logic has been proposed as means of providing a simple and intuitive formal account of truth that does not fall prey to paradoxes such as the Liar. However, such systems must also avoid Curry's paradox, which is much more difficult as it does not essentially involve negation. Set theory and the foundations of mathematics Epistemology and belief revision : Paraconsistent logic has been proposed as a means of reasoning with and revising inconsistent theories and belief systems. Knowledge management and artificial intelligence : Some computer scientists have utilized paraconsistent logic as a means of coping gracefully with inconsistentSee, for example, Truth maintenance systems or the articles in Bertossi et al. (2004). or contradictoryGershenson, C. (1999). Modelling emotions with multidimensional logic. In Proceedings of the 18th International Conference of the North American Fuzzy Information Processing Society (NAFIPS ’99), pp. 42–46, New York City, NY. IEEE Press. URL information. Deontic logic and metaethics : Paraconsistent logic has been proposed as a means of dealing with ethical and other normative conflicts. Software engineering : Paraconsistent logic has been proposed as a means for dealing with the pervasive inconsistencies among the documentation, use cases, and code of large software systems.Hewitt (2008b)Hewitt (2008a)Carl Hewitt. Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic Reasoning and the Actor Model. in Vol. 52 of Studies in Logic. College Publications. . 2015. Electronics design routinely uses a four-valued logic, with "hi-impedance (z)" and "don't care (x)" playing similar roles to "don't know" and "both true and false" respectively, in addition to True and False. This logic was developed independently of philosophical logics. Quantum physics Black hole physics Hawking radiation Quantum computing Spintronics Quantum entanglement Quantum coupling Uncertainty principle
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