Extensional higher order logic programming book

Higherorder logic programming holp languages are particularly useful for various kinds of metaprogramming and theorem proving tasks because of the logical support for variable binding via abstraction. What is the difference between intensional and extensional logic. Under this semantics, every program has a unique minimum herbrand model. Part of the lecture notes in computer science book series lncs, volume. In this chapter, we develop the idea of higher order logic programming by utilizing a higher order logic as the basis for computing. In this semantics program predicates denote sets of. In this paper the logic of broad necessity is explored. For example, higherorder hereditary harrop formulas hohh can be used to support aspects of modular programming, abstract data types, and higherorder programming. Leibniz basic notion of the truth of a judgment was that the concepts making up the predicate were included in the concept of the subject.

Intensional logic is an approach to predicate logic that extends firstorder logic, which has quantifiers that range over the individuals of a universe, by additional quantifiers that range over terms that may have such individuals as their value. It turns out that the extension of higherorder logic programs with constructive negation o ers a much greater versatility to extensional higherorder logic programming. Higher order logic programming holp languages are particularly useful for various kinds of meta programming and theorem proving tasks because of the logical support for variable binding via abstraction. It turns out that the extension of higher order logic programs with constructive negation o ers a much greater versatility to extensional higher order logic programming. Some extensional term models for combinatory logics and lambdacalculi. In other words, we provide a purely extensional theoretical framework for higher order logic programming which generalizes the familiar theory of classical first order logic programming.

Have you ever read an amazing book and did not solve the mystery itself. Dynamic assumptions are permitted and can be used during the execution. Some extensional term models for combinatory logics and lambdacalculi makes the reader have stronger analytical thinking skills. To appear in handbook of logic in ai and logic programming, d. First order semantics and expressiveness vernon asuncion, yan zhang, heng zhang. Annotation this book constitutes the refereed proceedings of the 5th international conference on elearning and games, edutainment 2010, held in changchun, china, in august 2010. Higherorder programming is a style of computer programming that uses software components, like functions, modules or objects, as values. But you can follow any of the programming books and there you will get better logic. A logic is extensional if whenever two predicates or two.

Intensional logic is an approach to predicate logic that extends first order logic, which has quantifiers that range over the individuals of a universe, by additional quantifiers that range over terms that may have such individuals as their value. We propose a purely extensional semantics for higherorder logic programming. Modularity can be built into a pure functional language objectedorientedness. Implementing default logic via answer set programming. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higherorder logic, that there is a broadest necessity, settling one of the central questions of this investigation. This book aims to show that a programming language based on a simply typed version of higher order logic provides an elegant, declarative means for providing such a treatment. In programming languages, firstorder functions similarly refer to functions that operate on individual data elements e. This book aims to show that a programming language based on a simply typed version of higherorder logic provides an elegant, declarative means for providing such a treatment.

Pfenning, automating higher order logic in automated theorem proving. Extensional semantics for higherorder logic programs with. Moreover, there exists a relative simple sound proof procedure for the new language. Higherorder logic and intuitionistic type theory overlaps in many ways. Three broad topics are covered in pursuit of this goal.

The distinction between intensional and extensional entities is parallel to the distinction between sense and reference. Objectoriented features require state updation and can be obtained only by destroying referential transparency. It turns out that the extension of higher order logic programs with constructive negation o ers a much greater versatility to extensional higherorder logic programming. Applications of lambda prolog in higherorder programming and metaprogramming.

In this way we provide an alternative extensional semantics for higherorder logic programs with negation to the one proposed in. From frege to g odel, a source book in mathematical. Secondorder and higherorder logic stanford encyclopedia of. Higher order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. Logic programming is based upon an extension of first order logic. They have been used for a wide range of applications including theorem proving, program. Extensional higherorder logic programming springerlink. Sections 7, 8 and 9 will be covered in lectures 6, 7 and 8. Welcome to the home page for the book programming with higherorder logic by dale miller and gopalan nadathur. Charalambidis a, handjopoulos k, rondogiannis p and wadge w 20 extensional higher order logic programming, acm transactions on computational logic tocl, 14. Reduce reduce is an interactive system for general algebraic computations of interest to mathematicians, sc.

First order logics, including set theory are all extensional in this sense. Higherorder logic programming languages such as prolog and twelf improve the notion of first order logic programming in two ways. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Download programming with higherorder logic pdf ebook. Unfortunately his work did not become widely known. In this speci cation, the variable n ranges over the numerals 0. Book title logics in artificial intelligence book subtitle 12th european conference, jelia 2010, helsinki, finland, september. First order logic is made up of syntax and semantics.

Create sophisticated triggers to provide notifications and alerts of conditions specific to your needs. Higherorder logic 243 for their own sake, and countable models of set theory are at the base of the independence proofs. Part ii demonstrates that another formulation of higher order logic, intuitionistic type theories, is closely related to topos theory. Proof procedures of extensional higherorder logic programming.

If youre looking for a free download links of programming with higherorder logic pdf, epub, docx and torrent then this site is not for you. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higherorder functions. We also propose an sldresolution proof procedure which is proven sound and complete with respect to the minimum model semantics. Citeseerx a extensional higherorder logic programming. Wadge abstract we describe a fragment of higherorder horn logic which can be used as a higherorder extension of prolog. Sep 26, 2016 there is no such books on programming logic. The intricacies of 3valued extensional semantics for higherorder logic programs article pdf available in theory and practice of logic programming. Firstorder semantics and expressiveness vernon asuncion, yan zhang, heng zhang. First, a prooftheoretic framework that supports a general view of logic programming is identified.

Jul 15, 2017 the intricacies of 3valued extensional semantics for higherorder logic programs article pdf available in theory and practice of logic programming july 2017 with 24 reads how we measure reads. Intensional logic stanford encyclopedia of philosophy. Under this semantics, every program has a unique minimum herbrand model which is the greatest lower bound of all herbrand models of the program and the least fixedpoint of the immediate consequence operator of the program. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher order functions. Logic programming is based upon an extension of firstorder logic. What are the best books for improving programming logic. Constructive negation in extensional higher order logic programming angelos charalambidis, panos rondogiannis. Gopalan nadathur and dale miller higherorder logic programming, technical report cs199438, department of computer science, duke university,1994. Semantics of negation in extensional higherorder logic. The wellfounded semantics is the principle of inductive definition.

It allows the programmer to axiomatize predicates of predicates and operations on predicates. Pdf the intricacies of 3valued extensional semantics for. Practical foundations for programming languages by robert. In this chapter, we develop the idea of higherorder logic programming by utilizing a higherorder logic as the basis for computing. Principles of knowledge representation and reasoning. Pdf the intricacies of 3valued extensional semantics. Higherorder logic is based on a manysorted language with a collection of sorts or types. Under this semantics, every program has a unique minimum herbrand.

Theory and practice of logic programming 14, 45, 725737. We develop an extensional semantics for higher order logic programs with negation, generalizing the technique that was introduced in 2, 3 for positive higher order programs. In part i, they show that typed lambdacalculi, a formulation of higher order logic, and cartesian closed categories, are essentially the same. We have designed and built a logic programming system which implements hohh in much the same way prolog implements firstorder horn clauses. Other articles where extensional logic is discussed. Moreover, every program has a unique minimum herbrand model which is the greatest lower bound of all herbrand models. Completeness is proved relative to an analog of henkin models, familiar for higher type classical logics. Iclp 2017 report association for logic programming. Under this semantics, every program has a unique minimum herbrand model which is the greatest lower bound of all. Mechanizing programming logics in higher order logic. Terms from the higherorder language are defined via abstraction. Pdf we propose a purely extensional semantics for higherorder logic programming. This book was published by cambridge university press in june 2012. As an immediate useful consequence of our developments, we define for the.

Higher order logic in relation to computing and programming. The most obvious is third, fourth, and so on order logic. Part ii demonstrates that another formulation of higherorder logic, intuitionistic type theories, is closely related to topos theory. Wadge abstract we describe a fragment of higher order horn logic which can be used as a higher order extension of prolog. Minimum model semantics for extensional higherorder logic programming with negation. We propose a purely extensional semantics for higher order logic programming. Higher order logic an overview sciencedirect topics. The syntax of first order logic is a formal language that is used to express concepts. Section 12 contains concluding remarks and a brief discussion of future work. Automated reasoning in higherorder logic presents both a theoretical analysis of fragments of higherorder logic as well as a complete automated search procedure for an extensional form of higherorder logic. If youre looking for a free download links of programming with higher order logic pdf, epub, docx and torrent then this site is not for you. As first order logic is well understood and can be mathematically provable it can be used for representing all computational problems. We can extend higher order logic programming with constructive negation. Mitchell foundations for programming languages, foundations of computing, mit press,1996.

We develop an extensional semantics for higherorder logic programs with negation, generalizing the technique that was introduced in 2, 3 for positive higher order programs. Intensional logic jaroslav peregrin 1 freges bedeutung the german mathematician and one of the founding fathers of modern logic, gottlob frege 18481925, was the first to clearly realize that semantics has little to do with psychology, and that it could be usefully explicated in mathematical terms see dummett, 1973. Review for theory and practice of logic programming. Higherorder logic programming in twelf extends traditional rstorder logic programming in three ways. The intricacies of threevalued extensional semantics for higher. Higher order logic and intuitionistic type theory overlaps in many ways. It doesnt matter whether we are talking about the set of the renates or the set of the cordates, because they are the same set, and we know theyre the same set, because we define a set extensionallyi.

An intensional logic, however we do need to know what the terms mean, because we want to ask not just about which things do, as a matter of contingent fact, happen to fall under those terms. Gopalan nadathur and dale miller higher order logic programming, technical report cs199438, department of computer science, duke university,1994. What is the difference between intensional and extensional. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher order logic, that there is a broadest necessity, settling one of the central questions of this investigation. We develop an extensional semantics for higherorder logic programs with negation, generalizing the technique that was introduced in 2, 3 for positive higherorder programs. Second, they have largely imported the notion of higherorder programming as it is understood within functional programming and have not examined a notion that is intrinsic to logic programming. Higherorder logic refers to all these logics that are more powerful than firstorder logic. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. Constructive negation in extensional higherorder logic programming angelos charalambidis, panos rondogiannis. We can extend higherorder logic programming with constructive negation. Higher order functions characterise most functional programming. In this way we provide an alternative extensional semantics for higher order logic programs with negation to the one proposed in.

Applications of lambda prolog in higher order programming and meta programming. In the second part of the book, an automated proof procedure for extensional type theory. Higher order logic programming languages such as prolog and twelf improve the notion of first order logic programming in two ways. Tichy created a system of intensional logic very similar to that of montague, beginning, in english, in tichy 1971, with a detailed presentation in tichy 1988. Terms from the higher order language are defined via abstraction. Troelstra, in studies in logic and the foundations of mathematics, 1998.

Second, they have largely imported the notion of higher order programming as it is understood within functional programming and have not examined a notion that is intrinsic to logic programming. Consequently, higherorder logic has become an important topic of research. Harpers book provides a comprehensive treatment of the foundations of computation. There are many ways to further extend secondorder logic. Under this semantics, every program has a unique minimum herbrand model which is the greatest lower bound of all herbrand models of the program and the least fixed. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The general principle, already recognized by tarski 1933 1956, is that in higher order logic one can formalize the semanticsdefine truthof lower order logic.