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Inductive definability in formal language theory

P.F. Schuler
1978 Journal of computer and system sciences (Print)  
INTRODUCTION Rewriting concepts of grammars used in existing formal language theory are various kinds of monadic inductive deiinabi1ity.l That is, in building up linguistic phenomena in stages, one is  ...  After all, formal language theory should explore communication between man and machine.  ... 
doi:10.1016/0022-0000(78)90025-9 fatcat:2flb4alar5cabnpxqpkr2bry5y

A Co-inductive Language and Truth Degrees [chapter]

Shunsuke Yatabe
2011 Lecture Notes in Computer Science  
We investigate what happens if PA LTr2, a co-inductive language, formalizes itself.  ...  We analyze the truth concept in fuzzy logics by formalizing truth degree theory in the framework of truth theories in fuzzy logics.  ...  the following people for their kind advice and discussions: Ryota Akiyoshi, Libor Behounek, Petr Cintula, Yasuo Deguchi, Yuko Murakami, Kengo Okamoto, Graham Priest, Kentaro Sato, Izumi Takeuti, and in  ... 
doi:10.1007/978-3-642-23211-4_13 fatcat:cotefhhu35bvhdbvj4phjlmycu

Structuring Metatheory on Inductive Definitions

David Basin, Seán Matthews
2000 Information and Computation  
We show how metatheories based on inductive definitions allow theories and general metatheorems to be organized this way and report on a case study using the theory FS 0 . ]  ...  We use the example of the deduction theorem for modal logic and show how a statement about a theory can explicitly formalize the closure conditions extensions should satisfy for it to remain true.  ...  In particular, it rules out arguments requiring induction on the structure of the language or proofs of a theory.  ... 
doi:10.1006/inco.2000.2858 fatcat:am3mm6zv2vegjf4syvnx2c7ifu

PhD Abstracts

GRAHAM HUTTON
2017 Journal of functional programming  
Many students complete PhDs in functional programming each year.  ...  The usual way of defining type theory formally is by starting with an inductive definition of precontexts, pretypes and preterms and as a second step defining a ternary typing relation over these three  ...  A part of constructive mathematics is type theory itself, hence we should be able to say what type theory is using the formal language of type theory.  ... 
doi:10.1017/s0956796817000089 fatcat:p2yk5sbqazcuriv33wdtzekcc4

Sets in homotopy type theory

EGBERT RIJKE, BAS SPITTERS
2015 Mathematical Structures in Computer Science  
We thus wonder whether those 'discrete' groupoids do in fact form a (predicative) topos. More generally, homotopy type theory is conjectured to be the internal language of 'elementary' of ∞-toposes.  ...  We prove that sets in homotopy type theory form a ΠW-pretopos. This is similar to the fact that the 0-truncation of an ∞-topos is a topos.  ...  types as the internal language for higher topos theory??  ... 
doi:10.1017/s0960129514000553 fatcat:hwv3rsgqdnev7bv2ek3ok6me7u

Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic [chapter]

Marc Denecker, Joost Vennekens
2008 Lecture Notes in Computer Science  
This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions.  ...  We discuss the relationship between inductive definitions and common sense reasoning and the strong similarities and striking differences with ASP and Abductive LP.  ...  ., the definitions, in FO(ID) compensate for FO's weakness on representing inductive definitions and common sense knowledge.  ... 
doi:10.1007/978-3-540-89982-2_12 fatcat:t6kp52j4sbcvlckquq5aae53gy

Troubles with (the concept of) truth in mathematics

Roman Murawski
2007 Logic and Logical Philosophy  
In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered.  ...  Connections between satisfaction and truth on the one hand and consistency of certain systems of ω-logic and transfinite induction on the other are indicated.  ...  formalized language L in L itself.  ... 
doi:10.12775/llp.2006.017 fatcat:cojhag4cmbdo7gacettp52om5m

Yablo-Like Paradoxes and Co-induction [chapter]

Shunsuke Yatabe
2011 Lecture Notes in Computer Science  
We show that is caused by the fact that co-inductive definitions of formulae are possible because of the existence of the truth predicate.  ...  Beall, Libor Behounek, Daisuke Bekki, Kengo Okamoto, John Power, Graham Priest, Greg Restall, Kentaro Sato, Takeshi Yamada, and in particular Petr Hájek.  ...  However, such languages are not so new: they have already appeared in the study of truth theories, for example.  ... 
doi:10.1007/978-3-642-25655-4_8 fatcat:37lrtpu53fcmvj6nr36zly36ee

On recursion

Jeffrey Watumull, Marc D. Hauser, Ian G. Roberts, Norbert Hornstein
2014 Frontiers in Psychology  
in systems of the formal and natural sciences.  ...  By these necessary and sufficient criteria, the grammars of all natural languages are recursive. The theory of recursive functions was propounded in the foundations of mathematics.  ...  to research on natural language [see Chomsky (2007) on the inapplicability of formal language theory to natural language].  ... 
doi:10.3389/fpsyg.2013.01017 pmid:24409164 pmcid:PMC3884515 fatcat:47leulchbnejrlxniv2wwe4rqa

Maude as a formal meta-tool [chapter]

M. Clavel, F. Durán, S. Eker, J. Meseguer, M. O. Stehr
1999 Lecture Notes in Computer Science  
This paper explains how the reflective logical framework of rewriting logic can be used, in conjunction with an efficient reflective implementation such as the Maude language, to design formal meta-tools  ...  This poses two important technical challenges: how to rigorously meet the need to interrelate formalisms, and how to reduce the duplication of effort in tool and specification building across formalisms  ...  discussions and extensive joint work on formal interoperability.  ... 
doi:10.1007/3-540-48118-4_39 fatcat:fefrfcvcafb2lih3jqxqudyacm

Foreword

John Case, Takeshi Shinohara, Thomas Zeugmann, Sandra Zilles
2008 Theoretical Computer Science  
research in Inductive Inference.  ...  shows his love for Learning Theory and Theoretical Computer Science -and in the way he conveys his seemingly inexhaustible knowledge to others.  ...  Though today an independent branch of machine learning research, the theory of online learning has some roots in common with the theory of Inductive Inference.  ... 
doi:10.1016/j.tcs.2008.02.020 fatcat:jftjiljzjbbmbo7uxva4ftfvqa

The Isabelle Framework [chapter]

Makarius Wenzel, Lawrence C. Paulson, Tobias Nipkow
2008 Lecture Notes in Computer Science  
Submitting formal theories there helps to maintain applications in the longer term, synchronized with the ongoing development of Isabelle itself.  ...  This includes (co)inductive sets [35] , inductive datatypes [11] , and recursive functions [42, 23] .  ...  ZF, formalized in Isabelle/ZF.  ... 
doi:10.1007/978-3-540-71067-7_7 fatcat:y75g4zyzmjdgbkmosmujtq7yra

Cognitive Binary Logic - The Natural Unified Formal Theory of Propositional Binary Logic

Nicolaie Popescu-Bodorin, Luminita State
2011 arXiv   pre-print
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs  ...  (demonstrability in Hilbertian acception), deduction (Gentzen's view of demonstrability), CNF-ization, and deconstruction to be expressed and tested in the same (computational) formal language, using  ...  This is what we usually call formalization and the result is a formal theory defined over a formal language.  ... 
arXiv:1106.2352v1 fatcat:neib2lzwfbdvzhve4pn2cxp3pq

Page 3202 of Mathematical Reviews Vol. , Issue 80H [page]

1980 Mathematical Reviews  
K. 80h:68005 Issues in the formal specification of programming languages. Formal description of programming concepts (Proc. IFIP Working Conf., St.  ...  Some early attempts to devise formal specification methods are presented eisewhere [Formal language description languages for computer programming (Proc.  ... 

Polytypic Programming in Maude

M. Clavel, F. Durán, N. Martí-Oliet
2000 Electronical Notes in Theoretical Computer Science  
The idea of polytypic programming is to write programs that are defined by induction on the structure of user-defined datatypes.  ...  In particular, we explain how to define in Maude two non-trivial generic functions, namely, the polytypic versions of the functions map and cata, and how to prove properties about them using an inductive  ...  See [5, 3] for details on defining strategy languages in Maude.  ... 
doi:10.1016/s1571-0661(05)80135-5 fatcat:wpq7lbbahzexxecmr4babjxcry
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