Hierarchies in independence logic
نویسندگان
چکیده
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential second-order logic.
منابع مشابه
Hierarchies in independence and inclusion logic with strict semantics
We study the expressive power of fragments of inclusion and independence logic defined by restricting the number k of universal quantifiers in formulas. Assuming the so-called strict semantics for these logics, we relate these fragments of inclusion and independence logic to sublogics ESOf (k∀) of existential second-order logic, which in turn are known to capture the complexity classes NTIMERAM...
متن کاملBayesian Network Learning with Abstraction Hierarchies and Context-Specific Independence
Context-specific independence representations, such as treestructured CPTs, reduce the number of parameters in Bayesian networks by capturing local independence relationships. We previously presented Abstraction-Based Search (ABS), a technique for using attribute value hierarchies during Bayesian network learning to remove unimportant dis-ion-Based Search (ABS), a technique for using attribute ...
متن کاملWhat's So Special About Kruskal's Theorem and the Ordinal Gamma0? A Survey of Some Results in Proof Theory
This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Kruskal’s tree theorem, and in particular the connection with the ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Veblen hierarchies, some subsystems of second-order logic, slow-growing and...
متن کاملOn Inheritance Hierarchies With Exceptions
Using default logic, we formalize NETL-like inheritance hierarchies with exceptions. This provides a number of benefits: (1) A precise semantics for such hierarchies. (2) A provably correct (with respect to the proof theory of default logic) inference algorithm for acyclic networks. (3) A guarantee that acyclic networks have extensions. (4) A provably correct quasi-parallel inference algorithm ...
متن کاملIndependence and Hintikka games
This paper investigates the formalization of independence in logic, in particular between quantifiers. We first illustrate that this form of independence plays a role in many fields. A logic that has the possibility to express such a form of independence is Independence Friendly logic (introduced by Hintikka); its semantics is defined by means of strategies in a sequential game. It will be show...
متن کامل