Abstract
This paper studies information changes in default justification logic with argumentation semantics. We introduce dynamic operators that combine belief revision and default theory tools to define both prioritized and non-prioritized operations of contraction, expansion and revision for justification logic-based default theories. This combination enriches both default logics and belief revision techniques. We argue that the kind of attack called “undermining” amounts to those operations that contract a knowledge base by an attacked formula.
I wish to thank Allard Tamminga, Barteld Kooi and Rineke Verbrugge for their useful advice on this project. My research is supported by Ammodo KNAW award Rational Dynamics and Reasoning.
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Notes
- 1.
In fact, ABA does not distinguish between different kinds of attacks and models each attack as that on premises or what we call here undermining. In ASPIC+, undermining is taken as a primitive notion of attack, which is different from rebuttal or undercut only by virtue of targeting “ordinary” premises of an argument.
- 2.
The first variant of justification logic, the logic of proofs (LP), was developed in [5]. The logic of non-defeasible and factive reasons that we use here was first defined in [10]. For more basic information on its relation to other justification logics see [17]. For recent overviews of justification logic systems, see [6] and [22].
- 3.
For example, one such constant specification set could be generated by assigning a Gödel number to each axiom instance and to each instance of R1.
- 4.
Formally, we also do not require that \(t = t'\) holds in the antecedent of condition (3) for the general definition of defaults above. This reflects the independence of the warrant \((u\cdot t):G\) from the data t : F to which we apply the warrant.
- 5.
The non-inferential view of information change is also relevant for human interaction. As Hlobil [21] argues, we can believe by accepting testimonies, but we cannot make inferences by merely accepting testimony. Two testimonies that contradict each other are to be, ceteris paribus, equally treated and the acceptance of new information is not the same process as inferentially extending the existing (incomplete) information.
- 6.
Proving Proposition 12 is straightforward. Details are omitted due to space limitations.
- 7.
Analogously, conservative expansion might not guarantee that there will be any extension containing a formula F, after a default theory has been conservatively expanded with F.
- 8.
If we were to exhaust all possible combinations, eight revision operators could be defined. Note that the revision operation symbols we use below reflect the composition of the introduced revision operations that are defined in terms of contraction and expansion variants. The symbols are not intended to be in continuity with the standard usage of revision operation symbols.
- 9.
Note that the second output theory \((_{[F]}T^-_{\lnot F})^{\times }_F\) of Definition 17 is an application-constrained default theory (\((_{[F]}T^-_{\lnot F})^+_F\) is, by our convention, a default theory after F has been added to the set of facts). The fact that \((_{[F]}T^-_{\lnot F})^{\times }_F\) is an application-constrained theory might cause problems if we want to make our operators global, rather than local, and enable iterated revision. A solution to this problem would be to allow for iterated contraction and generalize the contraction operation to application-constrained theories. This could be done if we allow that an application-constrained theory \(_{[F]}T\) can be further constrained by a formula G. We leave the details of developing iterated variants of the present operators for the future work.
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Pandžić, S. (2020). On the Dynamics of Structured Argumentation: Modeling Changes in Default Justification Logic. In: Herzig, A., Kontinen, J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2020. Lecture Notes in Computer Science(), vol 12012. Springer, Cham. https://doi.org/10.1007/978-3-030-39951-1_14
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