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On Rational Entailment for Propositional Typicality Logic [article]

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2018 arXiv   pre-print
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional  ...  In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor  ...  Introduction Propositional Typicality Logic (PTL) [2, 3] is a recently proposed logic allowing for the representation of and reasoning with an explicit notion of typicality.  ... 
arXiv:1809.10946v1 fatcat:ie4gy5swkfg7jarmrwcc2l67oi

On rational entailment for propositional typicality logic

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Artificial Intelligence  
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional  ...  In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor  ...  Introduction Propositional Typicality Logic (PTL) [1, 2] is a recently proposed logic allowing for the representation of and reasoning with an explicit notion of typicality.  ... 
doi:10.1016/j.artint.2019.103178 fatcat:6wtakpxhyza2bomgyllnpqxoka

PTL: A Propositional Typicality Logic [chapter]

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Lecture Notes in Computer Science  
We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality.  ...  Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds for rational consequence and belief revision on PTL.  ...  Propositional Typicality Logic We introduce now a propositional typicality logic, called PTL, which extends propositional logic with a typicality operator a (read 'bar').  ... 
doi:10.1007/978-3-642-33353-8_9 fatcat:mwucomtwcfe3vcp7nwaqa34bui

A Minimal Model Semantics for Nonmonotonic Reasoning [chapter]

Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca Pozzato
2012 Lecture Notes in Computer Science  
We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they  ...  This paper provides a general semantic framework for nonmonotonic reasoning, based on a minimal models semantics on the top of KLM systems for nonmonotonic reasoning.  ...  , axiom (RM) is called rational monotony and it characterizes the logic of rational entailment R.  ... 
doi:10.1007/978-3-642-33353-8_18 fatcat:x5rhh6p26bht3plyrw355sjvcy

Towards Rational Closure for Fuzzy Logic: The Case of Propositional Gödel Logic [chapter]

Giovanni Casini, Umberto Straccia
2013 Lecture Notes in Computer Science  
As a first step, we will characterise rational closure in the context of Propositional Gödel Logic. Proof. It follows the proof of the classical counterpart ([13], Proposition 6).  ...  In the field of non-monotonic logics, the notion of rational closure is acknowledged as a landmark and we are going to see whether such a construction can be adopted in the context of mathematical fuzzy  ...  as the entailment problem for propositional Gödel logic and the procedure can be implemented once a decision procedure for fuzzy logic entailment is at hand.  ... 
doi:10.1007/978-3-642-45221-5_16 fatcat:snajpj3lvjcvjdk2iokyxoyyye

Taking Defeasible Entailment Beyond Rational Closure [chapter]

Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Lecture Notes in Computer Science  
We present a systematic approach for extending the KLM framework for defeasible entailment.  ...  We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible  ...  entailment (i.e., | ≈) for a logic language that extends propositional logic with the defeasible implication connective |∼.  ... 
doi:10.1007/978-3-030-19570-0_12 fatcat:oddvnetg5zgqfnbnguvypr7gq4

Semantic Foundation for Preferential Description Logics [chapter]

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Lecture Notes in Computer Science  
We present representation results for the description logic ALC for both preferential and rational consequence relations.  ...  We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of  ...  Acknowledgments This work was partially funded by Project number 247601, Net2: Network for Enabling Networked Knowledge, from the FP7-PEOPLE-2009-IRSES call.  ... 
doi:10.1007/978-3-642-25832-9_50 fatcat:yqsn7tbff5aizh7zedinz5jlvu

Semantic characterization of rational closure: From propositional logic to description logics

L. Giordano, V. Gliozzi, N. Olivetti, G.L. Pozzato
2015 Artificial Intelligence  
We are grateful to the anonymous referees for their careful reading and constructive criticisms, which greatly helped us to improve the final version of our work.  ...  We first consider rational closure as defined by Lehman and Magidor [33] for propositional logic, and we provide a semantic characterization based on a minimal models mechanism on rational models.  ...  For any propositional formula A, if rank( A)≥ i, then 1) k M (A) ≥ i, and 2) if A | ∼ B is rationally entailed by C i , then M i satisfies A | ∼ B.Proof. By induction on i.  ... 
doi:10.1016/j.artint.2015.05.001 fatcat:udeyt6pzebfifnhuxh5ckzuz3y

A framework for a modular multi-concept lexicographic closure semantics [article]

Laura Giordano, Daniele Theseider Dupré
2020 arXiv   pre-print
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality.  ...  The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic  ...  Acknowledgement: We thank the anonymous referees for their helpful comments and suggestions. This research is partially supported by INDAM-GNCS Project 2019.  ... 
arXiv:2009.00964v2 fatcat:zlhzj3epynavpear2yghztr7ne

Laws of Non-Contradiction, Laws of the Excluded Middle, and Logics * [chapter]

Greg Restall
2004 The Law of Non-Contradiction  
However, in many paraconsistent logics, statement * Thanks to JC Beall, Daniel Nolan and Graham Priest for discussion on the topics raised in this paper.  ...  There is widespread acknowledgement that the law of non-contradiction is an important logical principle. However, there is less-than-universal agreement on exactly what the law amounts to.  ...  So, the class of propositions to be accepted on the basis of logic is closed upward under entailment.  ... 
doi:10.1093/acprof:oso/9780199265176.003.0005 fatcat:dbavbymlkrdftgbxylbcd7m3z4

Another perspective on Default Reasoning [article]

Daniel Lehmann
2002 arXiv   pre-print
It provides a logic of normal defaults that is different from the one proposed by R. Reiter and that is rich enough not to require the consideration of non-normal defaults.  ...  The lexicographic closure is essentially a rational extension of D, and of its rational closure, defined in a previous paper.  ...  to typicality, and 4. respect for specificity.  ... 
arXiv:cs/0203002v1 fatcat:4bp3gc3okrgbje5xmfawhatesi

A KLM Perspective on Defeasible Reasoning for Description Logics [chapter]

Katarina Britz, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Lecture Notes in Computer Science  
This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case.  ...  The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case.  ...  Lehmann and Magidor's construction for propositional logic [52] , the rational closure of a defeasible knowledge base KB is dened as follows:Denition 24 (Rational Closure).  ... 
doi:10.1007/978-3-030-22102-7_7 fatcat:jqmd6rc2pbbk5lz2guo2lugete

Preferential Reasoning for Modal Logics

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Electronical Notes in Theoretical Computer Science  
We also prove representation results for both preferential and rational consequence, which paves the way for effective decision procedures for modal preferential reasoning.  ...  We argue that our semantics constitutes the foundation on which to explore preferential reasoning in modal logics in general.  ...  However, as in the propositional case [19] , the obvious definition of modal rational closure based on modal rational entailment does not produce an appropriate result.  ... 
doi:10.1016/j.entcs.2011.10.006 fatcat:4bhmdz76ufa7rh7dho3zlpm3uq

On the KLM properties of a fuzzy DL with Typicality [article]

Laura Giordano
2021 arXiv   pre-print
The paper investigates the properties of a fuzzy logic of typicality.  ...  First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALC^FT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised.  ...  rational extension of ALC in [14] and for preferential and rational entailment in KLM approach [39] .  ... 
arXiv:2106.00390v2 fatcat:yn3hdr4zl5hk5p2dqo57oqbhla

The Contingency of Contingency

Stephan Leuenberger
2015 Journal of Philosophy  
Recall that the justification for (2) turned on anti-rationalism entailing the non-demonstrability of LIB, or ∀p (⎕p → Lp).  ...  Hence anti-rationalism entails ¬L(LIB). Since GC entails its conjunct, anti-rationalism, it also entails ¬L(LIB). Hence premise (2) is true as well.  ... 
doi:10.5840/jphil201511226 fatcat:v5zdqe6efvbspfqet367crfxvq
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