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Jonas Philipp Haldimann

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5 papers

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KER Journal 2025 Journal Article

Inductive inference from weakly consistent belief bases

Jonas Philipp Haldimann
Christoph Beierle
Gabriele Kern-Isberner

Abstract We consider nonmonotonic inferences from belief bases that contain conditionals enforcing some of the possible worlds to be infeasible and thus completely implausible. In contrast to belief bases satisfying the strong notion of consistency requiring every world to be at least somewhat plausible, we call such belief bases weakly consistent. First, we review the treatment of weakly consistent belief bases by the seminal approaches of p-entailment, which coincides with system P, and of system Z, which coincides with rational closure. Then we focus on c-inference, an inductive inference operator that has been shown to exhibit many desirable properties put forward for nonmonotonic reasoning. It is based on c-representations, which are a special kind of ranking model ordering worlds according to their plausibility. While c-representation is defined for strongly consistent belief bases only, in this article, we extend the notions of c-representation and of c-inference to cover also weakly consistent belief bases. We adapt a constraint satisfaction problem (CSP) characterizing c-representations to capture extended c-representations, and we show how this extended CSP can be used to characterize extended c-inference, providing a basis for its implementation. We show various properties of extended c-inference and in particular, we prove that also the extended notion of c-inference fully satisfies syntax splitting. Furthermore, we extend and evaluate credulous and weakly skeptical c-inference to weakly consistent belief bases and provide characterizations for them as CSPs.

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AAAI Conference 2023 Conference Paper

Conditional Syntax Splitting for Non-monotonic Inference Operators

Jesse Heyninck
Gabriele Kern-Isberner
Thomas Meyer
Jonas Philipp Haldimann
Christoph Beierle

Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.

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FLAP Journal 2023 Journal Article

Epistemic State Mappings among Ranking Functions and Total Preorders.

Jonas Philipp Haldimann
Christoph Beierle
Gabriele Kern-Isberner

Ranking functions, also called ordinal conditional functions (OCFs), and to- tal preorders on worlds (TPOs) are two common models for epistemic states that can represent conditional beliefs. To explore the connection between these frameworks, we consider mappings among TPOs and OCFs, i. e. , the models of both frameworks. We formalize this kind of mappings as epistemic state mappings. Furthermore, we introduce postulates concerning the preservation of notable properties under the application of these mappings; a prominent example of such a property is syntax splitting. Other postulates regard the compatibility with operations like marginalization and conditionalization. We evaluate the interrelationships among the postulates for epistemic state map- pings within and across the two frameworks, establishing dependencies as well as incompatibilities among postulates. Our results will be useful in particular for transferring methods and tools developed for OCF-based semantics to the TPO framework and the other way around.

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KR Conference 2023 Conference Paper

Finest Syntax Splittings of Ranking Functions and Total Preorders on Worlds

Jonas Philipp Haldimann
Christoph Beierle

The notion of syntax splitting was initially introduced by Parikh for belief sets, and one key observation is that every belief set has a unique finest syntax splitting, i. e. , a syntax splitting that refines every other syntax splitting of that belief set. Later, the notion of syntax splitting was extended to ranking functions and total preorders on worlds (TPOs), which are two common models for belief states in the context of iterated belief revision. In this paper, we prove that ranking functions also have unique finest syntax splittings, i. e. , every ranking function has a syntax splitting that refines all other syntax splittings of that ranking function. Using this, we can show that the syntax splittings of a ranking function κ are exactly the coarsenings of the finest splitting of κ. For TPOs we show that, in contrast to ranking functions, the coarsening of a syntax splitting of a TPO ⪯ is not necessarily a syntax splitting of ⪯. Despite that we can prove that every TPO has a unique finest syntax splitting that refines all other syntax splittings of that TPO.

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KR Conference 2020 Conference Paper

Syntax Splitting for Iterated Contractions

Jonas Philipp Haldimann
Gabriele Kern-Isberner
Christoph Beierle

Parikh developed the notion of syntax splitting to describe belief sets with independent parts. He also formulated a postulate demanding that belief revisions respect syntax splittings in belief sets. The concept of syntax splitting was later transferred to epistemic states with total preorders and ranking functions by Kern-Isberner and Brewka along with corresponding postulates for belief revisions. Besides revision, contraction is also a central operation in the field of general belief change. In this paper, we analyse belief contractions with respect to syntax splitting. Based on the work on syntax splitting for revision, we develop syntax splitting postulates for contractions on ranking functions, on epistemic states with total preorder, and on belief sets. Finally, we evaluate different contractions from the literature, namely moderate contraction, natural contraction, lexicographic contraction, and c-contractions with respect to the newly developed contraction postulates.

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