During my postdoc at TU Wien, I was a member of the project Fragment-Driven Belief Change, which aimed at studying belief change operation in non-standard fragments of classical logic, or non-classical formalisms like abstract argumentation.
In this paper we introduce a new approach for revising and merging consistent Horn formulae under minimal model semantics. Our approach is translation-based in the following sense: we generate a propositional encoding capturing both the syntax of the original Horn formulae (the clauses which appear or not in them) and their semantics (their minimal models). We can then use any classical revision or merging operator to perform belief change on the encoding. The resulting propositional theory is then translated back into a Horn formula. We identify some specific operators which guarantee a particular kind of minimal change. A unique feature of our approach is that it allows us to control whether minimality of change primarily relates to the syntax or to the minimal model semantics of the Horn formula. We give an axiomatic characterization of minimal change on the minimal model for this new setting, and we show that some specific translation-based revision and merging operators satisfy our postulates.
@inproceedings{ecai2016,title={Translation-Based Revision and Merging for Minimal Horn Reasoning},booktitle={22nd {E}uropean {C}onference on {A}rtificial {I}ntelligence ({ECAI} 2016)},author={Brewka, Gerhard and Mailly, Jean-Guy and Woltran, Stefan},year={2016},pages={734--742},}
Understanding the behavior of belief change operators for fragments of classical logic has received increasing interest over the last years. Results in this direction are mainly concerned with adapting representation theorems. However, fragment-driven belief change also leads to novel research questions. In this paper we propose the concept of belief distribution, which can be understood as the reverse task of merging. More specifically, we are interested in the following question: given an arbitrary knowledge base K and some merging operator Δ, can we find a profile E and a constraint μ, both from a given fragment of classical logic, such that Δμ(E) yields a result equivalent to K? In other words, we are interested in seeing if K can be distributed into knowledge bases of simpler structure, such that the task of merging allows for a reconstruction of the original knowledge. Our initial results show that merging based on drastic distance allows for an easy distribution of knowledge, while the power of distribution for operators based on Hamming distance relies heavily on the fragment of choice.
@inproceedings{ijcai2016,title={Distributing Knowledge into Simple Bases},booktitle={25th {I}nternational {J}oint {C}onference on {A}rtificial {I}ntelligence ({IJCAI} 2016)},author={Haret, Adrian and Mailly, Jean-Guy and Woltran, Stefan},year={2016},pages={1109--1115},}
Formalizing dynamics of argumentation has received increasing attention over the last years. While AGM- like representation results for revision of argumentation frameworks (AFs) are now available, similar results for the problem of merging are still missing. In this paper, we close this gap and adapt model-based propositional belief merging to define extension-based merging oper- ators for AFs. We state an axiomatic and a constructive characterization of merging operators through a fam- ily of rationality postulates and a representation theo- rem. Then we exhibit merging operators which satisfy the postulates. In contrast to the case of revision, we observe that obtaining a single framework as result of merging turns out to be a more subtle issue. Finally, we establish links between our new results and previous ap- proaches to merging of AFs, which mainly relied on ax- ioms from Social Choice Theory, but lacked AGM-like representation theorems.
@inproceedings{kr2016,author={Delobelle, J\'er\^ome and Haret, Adrian and Konieczny, S\'ebastien and Mailly, Jean-Guy and Rossit, Julien and Woltran, Stefan},title={Merging of Abstract Argumentation Frameworks},booktitle={15th {I}nternational {C}onference on {P}rinciples of {K}nowledge {R}epresentation and {R}easoning ({KR} 2016)},year={2016},pages={33--42},}
@inproceedings{nmr2016a,title={Distributing Knowledge into Simple Bases},booktitle={16th {I}nternational {W}orkshop on {N}on-{M}onotonic {R}easoning ({NMR} 2016)},author={Haret, Adrian and Mailly, Jean-Guy and Woltran, Stefan},year={2016},}
@inproceedings{nmr2016b,title={Using {E}nthymemes to {F}ill the {G}ap between {L}ogical {A}rgumentation and {R}evision of {A}bstract {A}rgumentation {F}rameworks},booktitle={16th {I}nternational {W}orkshop on {N}on-{M}onotonic {R}easoning ({NMR} 2016)},author={Mailly, Jean-Guy},year={2016},}
@inproceedings{iaf2016,title={How different are two argumentation semantics?},booktitle={10\`emes {J}ourn\'ees d'{I}ntelligence {A}rtificielle {F}ondamentale ({IAF} 2016)},author={Doutre, Sylvie and Mailly, Jean-Guy},year={2016},}