Ordered fragments of first-order logic

  title={Ordered fragments of first-order logic},
  author={Reijo Jaakkola},
  • Reijo Jaakkola
  • Published 14 March 2021
  • Computer Science, Philosophy, Mathematics
  • ArXiv
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 

Tables from this paper

Description logics as polyadic modal logics

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)

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

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

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.



A Survey of Decidable First-Order Fragments and Description Logics

A short survey of some of the less well-known, decidable fragments of first-order logic which all have in common that they generalise the standard translation of ALC to first- order logic.

Algebraic classifications for fragments of first-order logic and beyond

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.

Fluted Logic with Counting

This paper extends the fluted fragment by the addition of counting quantifiers, and shows that the resulting logic retains the finite model property, and that the satisfiability problem for its (m + 1)-variable sub-fragment is in m-NExpTime for all positive m.

Binding Forms in First-Order Logic

A hierarchy of four fragments focused on the Boolean combinations of these forms is described, showing that the less expressive one is already incomparable with several first-order limitations proposed in the literature, as the guarded and unary negation fragments.

On the Restraining Power of Guards

  • E. Grädel
  • Mathematics, Computer Science
    Journal of Symbolic Logic
  • 1999
It is proved that the satisfiability problems for the guarded fragment and the loosely guarded fragment of first-order logic are complete for deterministic double exponential time and that some natural, modest extensions of the guarded fragments are undecidable.

One-dimensional Fragment of First-order Logic

It is argued that the notions of one-dimensionality and uniformity together offer a novel perspective on the robust decidability of modal logics and the two-dimensional and non-uniform one-dimensional fragments are shown undecidable.

Separateness of Variables - A Novel Perspective on Decidable First-Order Fragments

The concept of separateness of variables is treated and its applicability to the classical decision problem is explored and it is demonstrated that for several prefix fragments, several guarded fragments, the two-variable fragment, and for the fluted fragment.

On the Decision Problem for Two-Variable First-Order Logic

Improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence, establishing that the satisfiability problem for FO2 is NEXPTIME-complete.

On Games and Computation

The principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence and the connection of the related general setting to logic and computation formalisms is discussed, with emphasis on Turing-complete logic based on game-theoretic semantics.