# Ordered fragments of first-order logic

@article{Jaakkola2021OrderedFO, title={Ordered fragments of first-order logic}, author={Reijo Jaakkola}, journal={ArXiv}, year={2021}, volume={abs/2103.08046} }

Using a recently introduced algebraic framework for classifying fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the ordered logic and the fluted logic by modifying some of their syntactical restrictions. 2012 ACM Subject Classification Theory of computation → Logic

## 5 Citations

### Description logics as polyadic modal logics

- Computer ScienceArXiv
- 2021

This work investigates the polyadic version of ALC extended with relational permutation operators and tuple counting and promotes a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities.

### Towards a Model Theory of Ordered Logics: Expressivity and Interpolation (Extended version)

- Computer ScienceMFCS
- 2022

Axiomatic bisimulations are employed to compare the relative expressive power of ordered logics, and to characterise the logics as bisimulation-invariant fragments of FO à la van Benthem, and the Craig Interpolation Property is studied.

### Uniform Guarded Fragments

- Mathematics, Computer ScienceFoSSaCS
- 2022

The uniform one-dimensional guarded fragment, which is a natural polyadic generalization of the guarded two-variable logic, has the Craig interpolation property and the satisfiability problem of uniform guarded fragment is NExpTime-complete.

### Complexity of Polyadic Boolean Modal Logics: Model Checking and Satisfiability

- Computer Science, MathematicsCSL
- 2023

The combined complexity of the model checking problem for the resulting logic is PTime -complete and the satisfiability problem of polyadic modal logic extended with negation on accessibility relations is Exp time -complete.

### Algebraic classifications for fragments of first-order logic and beyond

- Mathematics, Computer ScienceArXiv
- 2020

A research program based on an algebraic approach to systematic complexity classifications of fragments of first-order logic and beyond, which provides a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators.

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A research program based on an algebraic approach to systematic complexity classifications of fragments of first-order logic and beyond, which provides a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators.

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