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A Generalisation of AGM Contraction and Revision to Fragments of First-Order Logic

Zhiqiang Zhuang, Zhe Wang, Kewen Wang, James Delgrande
2019 The Journal of Artificial Intelligence Research  
Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics.  ...  AGM contraction and revision assume an underlying logic that contains propositional logic.  ...  that resulted from the contraction step.  ... 
doi:10.1613/jair.1.11337 fatcat:prcimkdh4bgfxihimfftgaj6k4

Belief revision in Horn theories

James P. Delgrande, Pavlos Peppas
2015 Artificial Intelligence  
Sentences of L H are true or false in an interpretation according to the standard rules in propositional logic. Truth of φ in w is denoted w |= φ.  ...  Both restrictions are redundant in the AGM approach, but not in the Horn case.  ...  This of course contradicts w i+k ≺ * w i . 2 As mentioned in the beginning of the proof, the next step is to define an extension of * which is total, and preserves the µ-minimal worlds, for all Horn formulas  ... 
doi:10.1016/j.artint.2014.08.006 fatcat:cemlqkyyrzcotbmn3znqyy5dby

Canonical Ground Horn Theories [chapter]

Maria Paola Bonacina, Nachum Dershowitz
2013 Lecture Notes in Computer Science  
We study the application of these notions in the context of propositional Horn theories -or Moore families -presented as implicational systems or associative-commutative rewrite systems, and in the context  ...  To maximize the chance that such a saturated presentation be finite, it should also be contracted in a suitable sense, in which case it is deemed canonical.  ...  Acknowledgements We thank Andreas Podelski, Andrei Voronkov and Reinhard Wilhelm for organizing the workshop in Harald's memory.  ... 
doi:10.1007/978-3-642-37651-1_3 fatcat:2i446mzm4vfing2vot32lfgks4

Inter-Definability of Horn Contraction and Horn Revision

Zhiqiang Zhuang, Maurice Pagnucco, Yan Zhang
2016 Journal of Philosophical Logic  
Abstract There have been a number of publications in recent years on generalising the AGM paradigm to the Horn fragment of propositional logic.  ...  We show that Horn contraction generated from Horn revision is always plausible whereas Horn revision generated from Horn contraction is, in general, implausible and, to regain plausibility, the generating  ...  Acknowledgments We thank Heng Zhang for some fruitful discussions in the early stage of this work and Sebastian Binnewies for proofreading the first draft.  ... 
doi:10.1007/s10992-016-9401-2 fatcat:qtyxe2mcq5fyppnexqj3oc4ryu

Univalent Higher Categories via Complete Semi-Segal Types [article]

Paolo Capriotti, Nicolai Kraus
2017 arXiv   pre-print
Given the first (n+3) levels of a semisimplicial type S, we can equip S with three properties: first, contractibility of the types of certain horn fillers; second, a completeness property; and third, a  ...  complete semi-Segal n-types is equivalent to the type of univalent n-categories in these cases.  ...  The back left column starts with graphs and adds composition structure in the first step, associativity in the next, and coherence for associativity (the pentagon) in the last step.  ... 
arXiv:1707.03693v4 fatcat:ru5xi37fz5bfvhm7x46xrr25ce

A Logical Characterization of Forward and Backward Chaining in the Inverse Method [chapter]

Kaustuv Chaudhuri, Frank Pfenning, Greg Price
2006 Lecture Notes in Computer Science  
on the Horn fragment.  ...  We have recently shown how Andreoli's focusing strategy can be adapted for the inverse method in linear logic.  ...  In the next two sections we will describe this correspondence in slightly more detail.  ... 
doi:10.1007/11814771_9 fatcat:d6mixqbhqjcrvbyums7strig2y

A Logical Characterization of Forward and Backward Chaining in the Inverse Method

Kaustuv Chaudhuri, Frank Pfenning, Greg Price
2008 Journal of automated reasoning  
on the Horn fragment.  ...  We have recently shown how Andreoli's focusing strategy can be adapted for the inverse method in linear logic.  ...  In the next two sections we will describe this correspondence in slightly more detail.  ... 
doi:10.1007/s10817-007-9091-0 fatcat:ine774q3n5gg7lroimrb7hjscq

A contractive version of a Schur–Horn theorem in II1 factors

M. Argerami, P. Massey
2008 Journal of Mathematical Analysis and Applications  
We prove a contractive version of the Schur-Horn theorem for submajorization in II 1 factors that complements some previous results on the Schur-Horn theorem within this context.  ...  We obtain a reformulation of a conjecture of Arveson and Kadison regarding a strong version of the Schur-Horn theorem in II 1 factors in terms of submajorization and contractive orbits of positive operators  ...  Therefore, by (1), Next we prove our main result, which complements Theorem 2.4 in the case of submajorization and contractive orbits. E A C M (b) σ -sot = Θ A (b) ∩ A + . (4) Proof.  ... 
doi:10.1016/j.jmaa.2007.03.095 fatcat:ahmmokydarg2tia27rcxijahuy

Minimal change: Relevance and recovery revisited

Márcio M. Ribeiro, Renata Wassermann, Giorgos Flouris, Grigoris Antoniou
2013 Artificial Intelligence  
Motivated by the fact that non-classical logics (like Description Logics or Horn logic) are increasingly being used in various applications, we study contraction for all monotonic logics, classical or  ...  Our work is another step towards the aim of exploiting the rich belief change literature for addressing the evolution problem in a larger class of logics.  ...  Belief change in the Horn fragment of classical propositional logic has been a hot topic in the past years.  ... 
doi:10.1016/j.artint.2013.06.001 fatcat:67rbbkflrffe3cuxfojkzuwi2y

Univalent higher categories via complete Semi-Segal types

Paolo Capriotti, Nicolai Kraus
2017 Proceedings of the ACM on Programming Languages  
Given the first (n + 3) levels of a semisimplicial type S, we can equip S with three properties: first, contractibility of the types of certain horn fillers; second, a completeness property; and third,  ...  Category theory in homotopy type theory is intricate as categorical laws can only be stated "up to homotopy", and thus require coherences.  ...  The back left column starts with graphs and adds composition structure in the first step, associativity in the next, and coherence for associativity (the pentagon) in the last step.  ... 
doi:10.1145/3158132 dblp:journals/pacmpl/CapriottiK18 fatcat:oti2nshn7fgi3isca7zycx2qkq

A Rational and Efficient Algorithm for View Revision in Databases

R. Delhibabu, G. Lakemeyer
2013 Applied Mathematics & Information Sciences  
We show that Horn knowledge base dynamics has interesting connection with kernel change and abduction.  ...  In this paper, we argue that to apply rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first of all, it should allow a certain part  ...  (KB * 7.2) is relevance policy that still can not permit rational revisions, so we need to go next step.  ... 
doi:10.12785/amis/070302 fatcat:vqchwxttrjahno6qjltsbue5ui

Belief revision within fragments of propositional logic

Nadia Creignou, Odile Papini, Reinhard Pichler, Stefan Woltran
2014 Journal of computer and system sciences (Print)  
Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention.  ...  So far, research in this direction has been mainly devoted to the Horn fragment of classical logic.  ...  This last step can be performed in polynomial time if ψ and µ are Horn formulas.  ... 
doi:10.1016/j.jcss.2013.08.002 fatcat:kkj5gm5w6rfvvhtq3zkxkg3cyq

Merging in the Horn Fragment

Adrian Haret, Stefan Rümmele, Stefan Woltran
2017 ACM Transactions on Computational Logic  
While several such results have been obtained for Horn revision and Horn contraction, merging of Horn theories has been neglected so far.  ...  A current research trend in belief change is concerned with tailored representation theorems for fragments of logic, in particular Horn logic.  ...  These postulates make a difference only in the Horn fragment, while in full propositional logic they are redundant. Proposition 4.  ... 
doi:10.1145/3043700 fatcat:6z7i7nsuhrcllay3hojfo7wxom

Computational Complexity of Deciding Provability in Linear Logic and its Fragments [article]

Florian Chudigiewitsch
2021 arXiv   pre-print
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction.  ...  This interpretation makes linear logic a useful tool for formalisation in mathematics and computer science.  ...  The next step is the simulation of connectives.  ... 
arXiv:2110.00562v1 fatcat:a6sidawnbjh5jpf2cvrermfrcy

Optimal evaluations of graph-like expressions

John Staples
1980 Theoretical Computer Science  
This paper is &he second in a three-part study of efficient evaluations of expression.  ...  The next two results show the point of the definition of sound contraction. Result 2.  ...  Next we consider a contraction G + H as above by means of the following two cases: Case 1.  ... 
doi:10.1016/0304-3975(80)90051-1 fatcat:upbrtttqqrhy3de6p4my4mfvs4
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