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Closure and Consistency Rationalities in Logic-Based Argumentation [chapter]

Phan Minh Dung, Phan Minh Thang
2011 Lecture Notes in Computer Science  
Prakken has developed this idea further for a richer logic.  ...  We then demonstrate that the logical closure and consistency properties are rested on a simple notion of a base of arguments from which the argument could be constructed in an indefeasible way (using the  ...  Let E be a complete extension of a logic-based argumentation framework LAF. Further let S be a base of a subset of E.  ... 
doi:10.1007/978-3-642-20832-4_3 fatcat:touhalnajzholklx6qj6fod23y

CCC – The Casl Consistency Checker [chapter]

Christoph Lüth, Markus Roggenbach, Lutz Schröder
2005 Lecture Notes in Computer Science  
We demonstrate the viability of CCC by an extended example taken from the Casl standard library of basic datatypes.  ...  CCC is a faithful implementation of a previously described consistency calculus. Its system architecture combines flexibility with correctness ensured by encapsulation in a type system.  ...  CCC's design follows the so-called LCF design [8] , where a rich logic (such as higher-order logic) is implemented by a small logical core of basic axioms and inference rules.  ... 
doi:10.1007/978-3-540-31959-7_6 fatcat:qgtv5vr2svd77jnel5shzaj7he

On the Consistency of a Plural Theory of Frege's Grundgesetze

Francesca Boccuni
2011 Studia Logica: An International Journal for Symbolic Logic  
Overview The aim of the paper is to provide a model-theoretic consistency proof for the predicative second-order system PG, which employs plural quantification and a formulation of Frege's infamous Basic  ...  It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.  ...  the axiom of extensionality.  ... 
doi:10.1007/s11225-011-9311-9 fatcat:v2uvvi6ckfhznbnu6zyknuqaym

A New Game Equivalence, its Logic and Algebra

Johan van Benthem, Nick Bezhanishvili, Sebastian Enqvist
2018 Journal of Philosophical Logic  
A new game equivalence, its logic and algebra van Benthem, J.; Bezhanishvili, N.; Enqvist, S.  ...  We also thank the two referees of this paper for their careful and helpful comments.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10992-018-9489-7 fatcat:igg6jwbgczb3ta4bclgn6ilpva

Introduction to Abstractionism [chapter]

Philip A. Ebert, Marcus Rossberg
2016 Abstractionism  
Richard Heck (1996) shows that Basic Law V is consistent in predicative second-order logic.  ...  is usually considered to be the culprit, Basic Law V, is in fact consistent in weak fragments of second-order logic.  ... 
doi:10.1093/acprof:oso/9780199645268.003.0001 fatcat:7hnnrnoy6fentb3fjtn3f4zkhe

Frege on Numbers

Erich H. Reck
2005 The Harvard Review of Philosophy  
That is to say, their objectivity is a basic assumption; it is fixed and not further reducible.  ...  that from a logical point of view numerical expression, just like names for extensions of concepts, have to be regarded as object names.  ... 
doi:10.5840/harvardreview200513210 fatcat:uizbnfef6raldiuiiojunh7xfy

On the protocol composition logic PCL

Cas Cremers
2008 Proceedings of the 2008 ACM symposium on Information, computer and communications security - ASIACCS '08  
We identify a number of problems with this logic as well as with extensions of the logic, as defined in [9, 13, 14, 17, 20, 21] .  ...  A recent development in formal security protocol analysis is the Protocol Composition Logic (PCL).  ...  It is not sufficient, even with the addition of further axioms, as we show below. DH extension of the proof system.  ... 
doi:10.1145/1368310.1368324 dblp:conf/ccs/Cremers08 fatcat:pkvw66irwzhepcvtmic7nplh6a

Page 60 of Bucknell Review Vol. 3, Issue 2 [page]

1952 Bucknell Review  
Thus the basic requirement of his system is logical fertility, and the degree of such fertility in a pure mathe- matical system is the main standard of its excellence, assuming the logical consistency  ...  And the further a mathematician can go with a logically deduced series of propo- sitions the better.  ... 

Some Extensions of Probabilistic Logic [article]

Su-shing Chen
2013 arXiv   pre-print
Certainly, we get Nilsson's probabilistic logic by further restricting to consistent interpretations.  ...  It is applicable to any logical system for which the consistency of a finite set of propositions can be established.  ...  Of course, we get Nilsson's probabilistic logic by further restricting to consistent interpretations.  ... 
arXiv:1304.3080v1 fatcat:dqaxaakbcvgx7ptw5tjxupz5oe

Page 618 of The Philosophical Review Vol. 62, Issue 4 [page]

1953 The Philosophical Review  
In addition there are three appendixes which deal with combinatory operators, some further extensions of the system, and self-reference in philosophy.  ...  Hence, consistency proofs are emphasized. (2) For philosophical reasons a theory of types is false and should be avoided. (3) A logical system should be strong enough to serve as a basis for all of mathematics  ... 

Page 224 of American Society of Civil Engineers. Collected Journals Vol. 17, Issue 4 [page]

2003 American Society of Civil Engineers. Collected Journals  
The PSL outer core consists of a small set of generic exten- sions, including subactivity extension, activity-occurrence ex- tension, and states extension.  ...  Due to its logic framework, PSL can potentially be used to check consistency of project infor- mation by using a reasoning tool (Cheng et al. 2003).  ... 

Ontology-based modelling of architectural styles

Claus Pahl, Simon Giesecke, Wilhelm Hasselbring
2009 Information and Software Technology  
The conceptual modelling of software architectures is of central importance for the quality of a software system.  ...  A rich modelling language is required to integrate the different aspects of architecture modelling, such as architectural styles, structural and behavioural modelling, into a coherent framework.  ...  In this terminology, the pipe-and-filter style is actually a refinement of the basic architectural type vocabulary. As the original types are not further constrained, the extension is consistent.  ... 
doi:10.1016/j.infsof.2009.06.001 fatcat:l7t66lrspfd3tmcildovkszv3m

The Distributed Ontology Language (DOL): Ontology Integration and Interoperability Applied to Mathematical Formalization [article]

Christoph Lange and Oliver Kutz and Till Mossakowski and Michael Grüninger
2012 arXiv   pre-print
It aims at providing a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies.  ...  Logic Repository), which provide the foundation for formalizing real-world notions such as spatial and temporal relations.  ...  The Distributed Ontology Language (DOL) -Overview An ontology in the Distributed Ontology Language (DOL) consists of modules formalized in basic ontology languages, such as OWL (based on description logic  ... 
arXiv:1204.5093v1 fatcat:wyaxjfoponebjg4vaaqejni5yy

Designing potential extensions from G-SRS to ChEBI to identify natural product-drug interactions

Sanya Bathla Taneja, Tiffany Callahan, Mathias Brochhausen, Mary Paine, Sandra Kane-Gill, Richard Boyce
2021 Zenodo  
In this study, we designed potential logical extensions to the Chemical Entities of Biological Interest (ChEBI) ontology that map information about NPs and NP constituents from the Global Substance Registration  ...  The potential logical extensions are the first step in advancing research related to NPDIs using biomedical ontologies and knowledge graphs.  ...  METHODS We used a three-step approach to design the logical extensions from the G-SRS to the ChEBI ontology.  ... 
doi:10.5281/zenodo.5736386 fatcat:wlue4bopejezlmz32bfgenlsgm

A tutorial on default logics

Grigoris Antoniou
1999 ACM Computing Surveys  
This paper provides a tutorial-style introduction to some important approaches of Default Logic.  ...  Default Logic is one of the most prominent approaches to nonmonotonic reasoning, and allows one to make plausible conjectures when faced with incomplete information about the problem at hand.  ...  Rational Default Logic Constrained Default Logic enforces joint consistency of the justifications of defaults that contribute to an extension, but goes one step further by requiring that the consequent  ... 
doi:10.1145/344588.344602 fatcat:u7c4nzh6obduboul4hywtbr5ta
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