# A Trichotomy in the Complexity of Propositional Circumscription

@inproceedings{Nordh2005ATI, title={A Trichotomy in the Complexity of Propositional Circumscription}, author={Gustav Nordh}, booktitle={Logic Programming and Automated Reasoning}, year={2005} }

Circumscription is one of the most important and well studied formalisms in the realm of nonmonotonic reasoning. The inference problem for propositional circumscription has been extensively studied from the viewpoint of computational complexity. We prove that there exists a trichotomy for the complexity of the inference problem in propositional variable circumscription. More specifically we prove that every restricted case of the problem is either \(\Pi_{\rm 2}^{\rm P}\)-complete, coNP-complete…

## 23 Citations

### The Complexity of Circumscriptive Inference in Post’s Lattice

- Computer Science, MathematicsTheory of Computing Systems
- 2010

It is shown that in the general case, unless P=NP, only literal theories admit polynomial-time algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference.

### Trichotomies in the Complexity of Minimal Inference

- Mathematics2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

It is proved that the complexity of the minimal inference problem for each of them has a trichotomy (between P, coNP-complete, and Π2P-complete); one of these results finally settles with a positive answer thetrichotomy conjecture of Kirousis and Kolaitis.

### Trichotomies in the Complexity of Minimal Inference

- MathematicsTheory of Computing Systems
- 2011

It is proved that the complexity of the minimal inference problem with unbounded queries has a trichotomy (between P, coNP-complete, and Pi_2^P-complete) and this result finally settles with a positive answer thetrichotomy conjecture of Kirousis and Kolaitis.

### The Complexity of Circumscriptive Inference in Post’s Lattice

- Computer ScienceTheory of Computing Systems
- 2011

It is shown that in the general case, unless P=NP, only literal theories admit polynomial-time algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference.

### Explicit Representations of Persistency for Propositional Action Theories

- Computer Science
- 2021

This work introduces two syntactic operators, allowing to represent different kinds of persistency, and considers the languages obtained from propositional logic by adding them at any level of nesting, and shows an interesting picture of diverse complexity results.

### Complexity of non-monotonic logics

- Computer ScienceBull. EATCS
- 2010

This survey considers a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription, and describes complexity results for fragments of logical languages obtained by restricting the allowed set of operators.

### Complexity of Default Logic on Generalized Conjunctive Queries

- Computer ScienceLPNMR
- 2007

This paper derives a complete classification of default logic reasoning problems by means of universal algebra tools using Post's clone lattice, and proves a trichotomy theorem for the existence of an extension, classifying this problem to be either polynomial, NP- complete, or Σ2P-complete, depending on the set of underlying Boolean connectives.

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