18 found
Order:
See also
Peter Verdee
Université Catholique de Louvain
  1.  91
    Adaptive Logics Using the Minimal Abnormality Strategy Are P 1 1 \Pi^1_1 -Complex.Peter Verdée - 2009 - Synthese 167 (1):93 - 104.
    In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is $\Pi _1^1 - complete$ . So, the complexity results in (Horsten and Welch, Synthese 158:41–60,2007) are mistaken for adaptive logics using the minimal abnormality strategy.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  2.  95
    Yes Fellows, Most Human Reasoning is Complex.Diderik Batens, Kristof De Clercq, Peter Verdée & Joke Meheus - 2009 - Synthese 166 (1):113-131.
    This paper answers the philosophical contentions defended in Horsten and Welch . It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  3.  44
    Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics.Peter Verdée - 2013 - Foundations of Science 18 (4):655-680.
    In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also the inconsistent (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  4.  5
    Obtaining infinitely many degrees of inconsistency by adding a strictly paraconsistent negation to classical logic.Peter Verdée - forthcoming - Synthese:1-35.
    This paper is devoted to a consequence relation combining the negation of Classical Logic ) and a paraconsistent negation based on Graham Priest’s Logic of Paradox ). We give a number of natural desiderata for a logic \ that combines both negations. They are motivated by a particular property-theoretic perspective on paraconsistency and are all about warranting that the combining logic has the same characteristics as the combined logics, without giving up on the radically paraconsistent nature of the paraconsistent negation. (...)
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5.  54
    A New Approach to Classical Relevance.Inge De Bal & Peter Verdée - 2015 - Studia Logica 103 (5):919-954.
    In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6. The Dynamics of Relevance: Adaptive Belief Revision.Peter Verdée & Frederik Van De Putte - 2012 - Synthese 187 (S1):1-42.
    This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh's axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  1
    Which Style of Reasoning to Choose in the Face of Conflicting Information?Joke Meheus, Peter Verdée & Christian Straßer - 2013 - Journal of Logic and Computation 26 (1):361–380.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  8.  6
    On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit.Diderik Batens, Christian Straßer & Peter Verdée - 2009 - Logique Et Analyse 52 (207):281-304.
  9.  15
    On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit.Diderik Batens, Christian Strasser & Peter Verdée - 2009 - Logique Et Analyse 52 (207):281-304.
    For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  5
    A Non-Transitive Relevant Implication Corresponding to Classical Logic Consequence.Peter Verdée, Inge De Bal & Aleksandra Samonek - 2019 - Australasian Journal of Logic 16 (2):10-40.
    In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11.  18
    Handling Inconsistencies in the Early Calculus: An Adaptive Logic for the Design of Chunk and Permeate Structures.Jesse Heyninck, Peter Verdée & Albrecht Heeffer - 2018 - Journal of Philosophical Logic 47 (3):481-511.
    The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism proposed by Brown and Priest in, 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of this application (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  12.  27
    A Generic Framework for Adaptive Vague Logics.Peter Verdée & Stephan van der Waart van Gulik - 2008 - Studia Logica 90 (3):385-405.
    In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  13.  5
    Paraconsistent Reasoning in Science and Mathematics: Introduction.Peter Verdée & Holger Andreas - 2016 - In Peter Verdée & Holger Andreas (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics. Heidelberg: Springer Verlag. pp. 1-17.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  14.  36
    A Generic Framework for Adaptive Vague Logics.Peter Verdée & Stephan der Waart van Gulivank - 2008 - Studia Logica 90 (3):385 - 405.
    In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  15.  15
    Nice Embedding in Classical Logic.Peter Verdée & Diderik Batens - 2016 - Studia Logica 104 (1):47-78.
    It is shown that a set of semi-recursive logics, including many fragments of CL, can be embedded within CL in an interesting way. A logic belongs to the set iff it has a certain type of semantics, called nice semantics. The set includes many logics presented in the literature. The embedding reveals structural properties of the embedded logic. The embedding turns finite premise sets into finite premise sets. The partial decision methods for CL that are goal directed with respect to (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  16.  15
    Modelling Def+Easible Reasoning by Means of Adaptive Logic Games.Peter Verdée - 2012 - Logic Journal of the IGPL 20 (2):417-437.
    In this article, I present a dynamic logic game for defeasible reasoning. I argue that, as far as defeasible reasoning is concerned, one should distinguish between practical and ideal rationality. Starting from the adaptive logic framework, I formalize both rationality notions by means of logic games. The presented adaptive logic games are based on (i) standard logic games on the one hand and (ii) dynamic proof procedures for adaptive logic on the other hand. The games are similar to standard logic (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  17.  9
    A Generic Framework for Adaptive Vague Logics.Peter Verdée & Stephan Gulik - 2008 - Studia Logica 90 (3):385-405.
    Direct download  
     
    Export citation  
     
    Bookmark  
  18.  6
    Logical Studies of Paraconsistent Reasoning in Science and Mathematics.Peter Verdée & Holger Andreas (eds.) - 2016 - Springer Verlag.
    In this book we present a collection of papers on the topic of applying paraconsistent logic to solve inconsistency related problems in science, mathematics and computer science. The goal is to develop, compare, and evaluate different ways of applying paraconsistent logic. After more than 60 years of mainly theoretical developments in many independent systems of paraconsistent logic, we believe the time has come to compare and apply the developed systems in order to increase our philosophical understanding of reasoning when faced (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark