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A Logical Study of Some Common Principles of Inductive Definition and its Implications for Knowledge Representation [article]

Marc Denecker and Bart Bogaerts and Joost Vennekens
2017 arXiv   pre-print
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation  ...  This paper is a formal study of some of the most common forms of inductive definitions found in scientific text: monotone inductive definition, definition by induction over a well-founded order and iterated  ...  In knowledge representation, it is widely recognized that definitions are an important form of human expert knowledge that should be supported in knowledge representation and specification logics (Brachman  ... 
arXiv:1702.04551v1 fatcat:e5jnp72zprespgmnfvvf7qcm3e

A note on the Declarative reading(s) of Logic Programming [article]

Marc Denecker
2000 arXiv   pre-print
One common view is that logic programming is a logic for default reasoning, a sub-formalism of default logic or autoepistemic logic. In this view, negation as failure is a modal operator.  ...  This paper analyses the declarative readings of logic programming. Logic programming - and negation as failure - has no unique declarative reading.  ...  To some extend, a generalised form of non-monotone induction have been studied in the area of inductive definitions, the so called Iterated Inductive Definitions (Feferman 1970) .  ... 
arXiv:cs/0003056v1 fatcat:r3ihirojojfcvpfsibut2n3brm

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.  ...  This logic is a natural integration of classical logic and logic programming based on the view of a logic program as a definition.  ...  Thus, the "logic programs", i.e., 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

Logic programming revisited: logic programs as inductive definitions

Marc Denecker, Maurice Bruynooghe, Victor Marek
2001 ACM Transactions on Computational Logic  
The thesis is developed that logic programming can be understood as a natural and general logic of inductive definitions.  ...  This paper investigates the problem and proposes an alternative epistemological foundation for the canonical model approach, which is not based on common sense but on a solid mathematical information principle  ...  Apt for his encouragement as well as a number of valuable suggestions. The anonymous referees suggested a number of improvements.  ... 
doi:10.1145/383779.383789 fatcat:ndazuobvzvfzjf53wm5fnswj2y

Logic of induction: a dead horse? some thoughts on the logical foundations of probability

Ricardo Sousa Silvestre
2010 Princípios  
Utilizaremos para isso um conceito de probabilidade presente no Logical Foudations of Probability de Carnap chamada por ele de probabilidade pragmática.  ...  De forma a realizar isso, nos apoiaremos na distinçáo entre o problema da justificaçáo da induçáo e o problema da descriçáo da induçáo.  ...  Its purpose is rather to serve as a framework for representing inductive implications and drawing the plausible hypotheses entailed by them in a specific knowledge situation.  ... 
doaj:8fcaa873da504cb6a4f902d6a0e24e37 fatcat:pgm3v25se5gxtiou7ksok3zk2a

LOGICISM, INTERPRETABILITY, AND KNOWLEDGE OF ARITHMETIC

SEAN WALSH
2014 The Review of Symbolic Logic  
This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the  ...  Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical  ...  Representability Premise: It is known that the arithmetical principles are representable in the logical principles.  ... 
doi:10.1017/s1755020313000397 fatcat:sa46d557ovaazbrgrrfxcufh3q

Answer Set Programming's Contributions to Classical Logic [chapter]

Marc Denecker, Joost Vennekens, Hanne Vlaeminck, Johan Wittocx, Maurice Bruynooghe
2011 Lecture Notes in Computer Science  
Much research in logic programming and non-monotonic reasoning originates from dissatisfaction with classical logic as a knowledge representation language, and with classical deduction as a mode for automated  ...  In this paper, a look at different aspects of ASP, in an effort to identify precisely the limitations of classical logic that they exposed and investigate how the ASP approaches can be transferred back  ...  The wellfounded semantics formalizes the most common forms of inductive definitions such as monotone inductive definitions (e.g., reachability) and (non-monotone) definitions by induction over a well-founded  ... 
doi:10.1007/978-3-642-20832-4_2 fatcat:yrydik5mlrgmxd7azmhpuudz7i

Page 1687 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Symbolic Logic 68 (2003), no. 1, 163-186. To study the role of (common) knowledge in game theoretical de- cision making, epistemic logics of shallow depths have been devel- oped.  ...  The operators of standard temporal logic can be determined in an obvious way using inductive definitions. In contrast, inductive definitions of chop and projection are inherently more complex.  ... 

Inferential Theory of Learning as a Conceptual Basis for Multistrategy Learning [chapter]

Ryszard S. Michalski
1993 Multistrategy Learning  
To this end, this chapter introduces the Inferential Theory of Learning that provides a conceptual framework for explaining logical capabilities of learning strategies, i.e., their competence.  ...  V iewing learning as a process of modifying the learner's knowledge by exploring the learner's experience, the theory postulates that any such process can be described as a search in a knowledge space,  ...  Table of Symbols, Abbreviations and Definitions of Fundmental Concepts Logical implication or unidirectional mutual implication A ⇔ Β: α, β Mutual dependency (or m -dependency) between A and B; if A and  ... 
doi:10.1007/978-1-4615-3202-6_2 fatcat:3z4yxkxg3ndunpwth5h4lqmpam

On Teaching Demography: Some Non-traditional Guidelines [chapter]

Thomas K. Burch
2017 Demographic Research Monographs  
It also has many implications for the teaching of demography, some of them at odds with current practice.  ...  Taken as a whole it constitutes a toolbox of many theoretical models, some simple, some complex, some useful for one purpose, another for other purposes.  ... 
doi:10.1007/978-3-319-65433-1_13 fatcat:7xb772olejhgfmrwix4dokyrm4

FO(ID) as an extension of DL with rules

Joost Vennekens, Marc Denecker, Maurice Bruynooghe
2010 Annals of Mathematics and Artificial Intelligence  
In this paper, we observe that the logic FO(ID), which was developed as an integration of ASP and classical logic, provides an interesting source of inspiration for such extensions.  ...  In particular, it seems well-suited as an upperbound to a hierarchy of increaslingly expressive extensions of DL with rules.  ...  FO(ID) is a knowledge representation language that adds inductive definitions to first-order logic.  ... 
doi:10.1007/s10472-010-9207-9 fatcat:z6x4g3fatbcsfi32qmllplqtei

FO(ID) as an Extension of DL with Rules [chapter]

Joost Vennekens, Marc Denecker
2009 Lecture Notes in Computer Science  
In this paper, we observe that the logic FO(ID), which was developed as an integration of ASP and classical logic, provides an interesting source of inspiration for such extensions.  ...  In particular, it seems well-suited as an upperbound to a hierarchy of increaslingly expressive extensions of DL with rules.  ...  FO(ID) is a knowledge representation language that adds inductive definitions to first-order logic.  ... 
doi:10.1007/978-3-642-02121-3_30 fatcat:7ymvsia3fzhxld2rxn2slb4nga

A logic of nonmonotone inductive definitions

Marc Denecker, Eugenia Ternovska
2008 ACM Transactions on Computational Logic  
This paper discusses the formalisation of different forms of (non-)monotone induction by the well-founded semantics and illustrates the use of the logic for formalizing mathematical and common-sense knowledge  ...  in a new logic for Non-Monotone Inductive Definitions (ID-logic).  ...  with common-sense knowledge representation principles; the mathematical tools developed here serve to clarify the meaning of inductive definitions expressed in ID-logic.  ... 
doi:10.1145/1342991.1342998 fatcat:265gngzzhnealdwfqk6v3mjqre

Automated Inferencing

W. Bibel
1985 Journal of symbolic computation  
The emphasis is on a clarification of some or the main principles rather than on an exhaustive listing of particular techniques .  ...  It addresses classical deductive reasoning as well as non-monotonic and inductive reasoning. Several important reasoning methods are informally described and illustrated .  ...  and study of formalisms for the representation of knowledge and inference .  ... 
doi:10.1016/s0747-7171(85)80034-1 fatcat:5ygzcp2a3reszeakjzq4qaknla

Inductive Logic Programming: Theory and methods

Stephen Muggleton, Luc de Raedt
1994 The Journal of Logic Programming  
Stephen Muggleton is a Research Fellow of Wolfson College Oxford and Luc De Raedt is a Post-Doctoral Researcher of the Belgian National Fund for Scientific Research.  ...  The authors would especially like to thank Maurice Bruynooghe of the Katholieke Universiteit Leuven and Lincoln Wallen of Oxford University Computing Laboratory for useful input during this research.  ...  From computational logic, inductive logic programming inherits its representational formalism, its semantical orientation, and various well-established techniques.  ... 
doi:10.1016/0743-1066(94)90035-3 fatcat:v2trhpjg7jglxcstjpooffzaey
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