Some Turing-Complete Extensions of First-Order Logic

Kuusisto, Antti

doi:10.4204/eptcs.161.4

Cited by 10 publications

(44 citation statements)

References 19 publications

(22 reference statements)

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“…A rather tame such an operator, i.e., a modifier, is employed in [21] in order to obtain a Turing complete logic L (see [21] for the syntax and semantics). A possible reading of an L-formula ϕ states that it is possible to verify ϕ.…”

Section: There Exists An Assignment S Such Thatmentioning

confidence: 99%

A Double Team Semantics for Generalized Quantifiers

Kuusisto

2015

J of Log Lang and Inf

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We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic which canonically fuses together two-variable dependence logic and two-variable logic with counting quantifiers. We establish that the satisfiability and finite satisfiability problems of are complete for .

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Section: There Exists An Assignment S Such Thatmentioning

confidence: 99%

A Double Team Semantics for Generalized Quantifiers

Kuusisto

2015

J of Log Lang and Inf

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“…Firstly, it would be interesting to understand new clocking patterns in general, in addition to the finitely bounded, the f -bounded and the free semantics discussed above. These investigations could naturally be pushed to involve more general logics beyond modal logic, possibly containing, e.g., operators that modify the underlying models, and thereby directly linking to the research on the general logical framework of [19] and the research program of [19] and [20].…”

Section: Discussionmentioning

confidence: 99%

“…Thus the games are not determined, i.e., it is possible that neither player has a winning strategy (consider, e.g., the formula µX X ). This free semantics for modal logic results in a system that is essentially directly a fragment of the general, Turing-complete logic L of [19]. On the other hand, the different "clocking scenarios" described above (and further variants thereof) can be naturally imposed on L , and it would indeed make sense to study related phenomena in that framework.…”

Section: Variants With Ptime Model Checkingmentioning

confidence: 99%

Bounded Game-Theoretic Semantics for Modal Mu-Calculus and Some Variants

Hella¹,

Kuusisto²,

Rönnholm³

2020

Electron. Proc. Theor. Comput. Sci.

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We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.

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“…The striking simplicity of D * and the link between team semantics and gametheory make D * a particularly interesting system. There of course exist other logical frameworks where RE can be easily captured, such as abstract state machines [8], [1] and the recursive games of [12]. However, D * provides a simple unified perspective on recent advances in descriptive complexity based on team semantics.…”

Section: Introductionmentioning

confidence: 99%

“…However, D * provides a simple unified perspective on recent advances in descriptive complexity based on team semantics. The framework of [12] resembles D * since it provides a perspective on RE that explains computational notions via game-theoretic concepts, but the approach in [12] uses potentially infinite games (and the article [12] also lacks a compositional approach). The approach provided by D * is different.…”

Section: Introductionmentioning

confidence: 99%

Team Semantics and Recursive Enumerability

Kuusisto

2014

Preprint

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It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities for descriptive complexity theory. In order to properly understand the connection between team semantics and descriptive complexity, we introduce an extension D * of dependence logic that can define exactly all recursively enumerable classes of finite models. Thus D * provides an approach to computation alternative to Turing machines. The essential novel feature in D * is an operator that can extend the domain of the considered model by a finite number of fresh elements. Due to the close relationship between generalized quantifiers and oracles, we also investigate generalized quantifiers in team semantics. We show that monotone quantifiers of type (1) can be canonically eliminated from quantifier extensions of first-order logic by introducing corresponding generalized dependence atoms.

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Some Turing-Complete Extensions of First-Order Logic

Cited by 10 publications

References 19 publications

A Double Team Semantics for Generalized Quantifiers

A Double Team Semantics for Generalized Quantifiers

Bounded Game-Theoretic Semantics for Modal Mu-Calculus and Some Variants

Team Semantics and Recursive Enumerability

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