* Many-valued logics

* Many-valued logic, including fuzzy logic, which rejects the law of the excluded middle and allows as a truth value any real number between 0 and 1.

* Cignoli, R. L. O., D ' Ottaviano, I. M. L., Mundici, D. ( 2000 ) Algebraic Foundations of Many-valued Reasoning.

* Stanford Encyclopedia of Philosophy: " Many-valued logic " -- by Siegfried Gottwald.

Logics formalizing default reasoning can be roughly divided in two categories: logics able to deal with arbitrary default assumptions ( default logic, defeasible logic / defeasible reasoning / argument ( logic ), and answer set programming ) and logics that formalize the specific default assumption that facts that are not known to be true can be assumed false by default ( closed world assumption and circumscription ).

For example, both philosophers of language and semanticists make use of propositional, predicate and modal logics to express their ideas about word meaning ; what Frege termed ' sense '.

Hybrid logics have many features in common with temporal logics ( which use nominal-like constructs to denote specific points in time ), and they are a rich source of ideas for researchers in modern modal logic.

The involutiveness of negation is an important characterization property for logics and the corresponding varieties of algebras.

Structads are an approach to the semantics of logic that are based upon generalising the notion of sequent along the lines of Joyal's combinatorial species, allowing the treatment of more drastically nonstandard logics than those described above, where, for example, the ',' of the sequent calculus is not associative.

#* The notion of institution has been developed as an abstract formalization of the notion of logical system, with the goal of handling the " population explosion " of logics used in formal methods.

Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences.

The rule is valid with respect to the semantics of classical logic ( as well as the semantics of many other non-classical logics ), in the sense that if the premises are true ( under an interpretation ) then so is the conclusion.

Those most popular in the literature are three-valued ( e. g., Łukasiewicz's and Kleene's ), which accept the values " true ", " false ", and " unknown ", finite-valued with more than three values, and the infinite-valued ( e. g. fuzzy logic and probability logic ) logics.

The difference between the principle and the law is important because there are logics which validate the law but which do not validate the principle.

This particular deviation is disputed by some if only because E. F. Codd himself eventually advocated the use of special marks and a 4-valued logic, but this was based on his observation that there are two distinct reasons why one might want to use a special mark in place of a value, which led opponents of the use of such logics to discover more distinct reasons and at least as many as 19 have been noted, which would require a 21-valued logic.

It is vital to know which modal logics are sound and complete with respect to a class of Kripke frames, and for them, to determine which class it is.

There are Kripke incomplete normal modal logics, which is unproblematic, because most of the modal systems studied are complete of classes of frames described by simple conditions.

Carlson models are easier to visualize and to work with than usual polymodal Kripke models ; there are, however, Kripke complete polymodal logics which are Carlson incomplete.

Indeed, the first two forms above will yield vacuous truth in any logic that uses material conditional, but there are other logics which do not.

* Computability logic is a semantically constructed formal theory of computability, as opposed to classical logic, which is a formal theory of truth ; integrates and extends classical, linear and intuitionistic logics.

Isabelle is generic: it provides a meta-logic ( a weak type theory ), which is used to encode object logics like First-order logic ( FOL ), Higher-order logic ( HOL ) or Zermelo – Fraenkel set theory ( ZFC ).

Not all non-classical logics fall into this class, e. g. Modal logic is a non-classical logic which, however, has only two truth values.

This is contrasted with the more commonly known bivalent logics ( such as classical sentential or boolean logic ) which provide only for true and false.

Generally in non-classical logics, negation which satisfies the law of double negation is called involutive.

Examples of logics which have involutive negation are Kleene and Bochvar three-valued logics, Łukasiewicz many-valued logic, fuzzy logic IMTL, etc.

The belief revision approach is alternative to paraconsistent logics, which tolerate inconsistency rather than attempting to remove it.

Linear logic, in which duplicated hypotheses ' count ' differently from single occurrences, leaves out both of these rules, while relevant ( or relevance ) logics merely leaves out the latter rule, on the ground that B is clearly irrelevant to the conclusion.

OWL took DAML + OIL as a starting language ( which itself is built on top of RDF and XML ) and provided extensions that are compatible with description logics.

On the other hand the film as the object of knowledge challenges the usual transitivity on which all the other cinema was based, " undoing its cornerstones: space and time continuity, narrative and grammatical logics, the self-evidence of the represented worlds.

Examples of higher order logics include HOL, Church's Simple Theory of Types, Thierry Coquand's calculus of constructions, which allows for both dependent and polymorphic types.

There are a number of provability logics, some of which are covered in the literature mentioned in the References section.

By extension, the term noncommutative logic is also used by a number of authors to refer to a family of substructural logics in which the exchange rule is inadmissible.

Instead of simultaneous access, as in other modal logics, temporal logic accesses before or after.

Issues such as this have also been addressed in various temporal logics, where one can assert that " Eventually, either there will be a sea battle tomorrow, or there won't be.

The properties to be verified are often described in temporal logics, such as linear temporal logic ( LTL ) or computational tree logic ( CTL ).

" Non-classical " logics such as linear logic and temporal logics can also be used in logical inference, not just in model checking.

Covers many varieties of modal logics, e. g. temporal, epistemic, dynamic, description, spatial from a unified perspective with emphasis on computer science aspects, e. g. decidability and complexity.

Computation tree logic is in a class of temporal logics that include linear temporal logic ( LTL ).

Some of these logics, such as linear temporal logic and computational tree logic, allow assertions to be made about the sequences of states that a concurrent system can pass through.

#* Predicate logic and logical frameworks are used for proving programs correct, and logics such as temporal logic and # Fundamental concepts in computer science that are naturally expressible in formal logic.

Instead of dealing with infinite sequences of state, interval temporal logics deal with finite sequences.

Interval temporal logics find application in computer science, artificial intelligence and linguistics.

Such systems can be based on logics more complicated than simple propositional epistemic logic, see Wooldridge Reasoning about Artificial Agents, 2000 ( in which he uses a first-order logic incorporating epistemic and temporal operators ) or van der Hoek et al.