David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
A logic is called higher order if it allows for quantiﬁcation (and possibly abstraction) over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic (often also called type theory or the Theory of Types) began with Frege, was formalized in Russell  and Whitehead and Russell  early in the previous century, and received its canonical formulation in Church .1 While classical type theory has since long been overshadowed by set theory as a foundation of mathematics, recent decades have shown remarkable comebacks in the ﬁelds of mechanized reasoning (see, e.g., Benzm¨.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2013). Completeness in Hybrid Type Theory. Journal of Philosophical Logic (2-3):1-30.
Similar books and articles
Paul C. Gilmore (2001). An Intensional Type Theory: Motivation and Cut-Elimination. Journal of Symbolic Logic 66 (1):383-400.
William M. Farmer (1990). A Partial Functions Version of Church's Simple Theory of Types. Journal of Symbolic Logic 55 (3):1269-1291.
Paul Oppenheimer & Edward N. Zalta (2011). Relations Vs Functions at the Foundations of Logic: Type-Theoretic Considerations. Journal of Logic and Computation 21:351-374.
William M. Farmer (1995). Reasoning About Partial Functions with the Aid of a Computer. Erkenntnis 43 (3):279 - 294.
Martin Hofmann (1997). An Application of Category-Theoretic Semantics to the Characterisation of Complexity Classes Using Higher-Order Function Algebras. Bulletin of Symbolic Logic 3 (4):469-486.
Bart Jacobs (1989). The Inconsistency of Higher Order Extensions of Martin-Löf's Type Theory. Journal of Philosophical Logic 18 (4):399 - 422.
Jaakko Hintikka (2009). A Proof of Nominalism: An Exercise in Successful Reduction in Logic. In A. Hieke & H. Leitgeb (eds.), Reduction - Abstraction - Analysis. Ontos
S. Awodey & C. Butz (2000). Topological Completeness for Higher-Order Logic. Journal of Symbolic Logic 65 (3):1168-1182.
Added to index2009-01-28
Total downloads28 ( #109,369 of 1,725,159 )
Recent downloads (6 months)5 ( #134,554 of 1,725,159 )
How can I increase my downloads?