Transparent intensional logic (frequently abbreviated as TIL) is a
logical system
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system.
A for ...
created by
Pavel Tichý. Due to its rich ''procedural semantics'' TIL is in particular apt for the logical analysis of natural language. From the formal point of view, TIL is a hyperintensional, partial,
typed lambda calculus
A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a ...
.
TIL applications cover a wide range of topics from
formal semantics,
philosophy of language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy of language), meanin ...
,
epistemic logic,
philosophical
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, and
formal logic. TIL provides an overarching semantic framework for all sorts of discourse, whether colloquial, scientific, mathematical or logical. The semantic theory is a procedural one, according to which sense is an abstract, pre-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure.
TIL procedures, known as ''constructions'', are hyperintensionally individuated. Construction is the single most important notion of transparent intensional logic, being a philosophically well-motivated and formally worked-out conception of
Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic p ...
’s notion of mode of presentation. Constructions, and the entities they construct, are organized into a ramified type theory incorporating a simple type theory. The semantics is tailored to the hardest case, as constituted by hyperintensional contexts, and generalized from there to intensional and
extensional context In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in wh ...
s. The underlying logic is a Frege-style function/argument one, treating functions, rather than relations or sets, as primitive, together with a
Church
Church may refer to:
Religion
* Church (building), a building for Christian religious activities
* Church (congregation), a local congregation of a Christian denomination
* Church service, a formalized period of Christian communal worship
* Chri ...
-style logic, centred on the operations of functional abstraction and
application
Application may refer to:
Mathematics and computing
* Application software, computer software designed to help the user to perform specific tasks
** Application layer, an abstraction layer that specifies protocols and interface methods used in a c ...
.
Key constraints informing the TIL approach to
semantic analysis are ''compositionality'' and ''anti-contextualism''. The assignment of constructions to expressions as their meanings is context-invariant. Depending on the sort of logical context in which a construction occurs, what is context-dependent is the logical manipulation of the respective meaning itself rather than the meaning assignment.
See also
*
Intensional logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals ...
Bibliography
* P. Tichý (1988): ''The Foundations of Frege's Logic''. De Gruyter, Berlin and New York 1988, 333 pp.
* M. Duží, B. Jespersen and P. Materna:
Procedural Semantics for Hyperintensional Logic Foundations and Applications of TIL.'' Springer, 2010.
External links
TIL home page
Philosophical logic
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