Related papers: Logics for complexity classes
We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…
We study modal team logic MTL, the team-semantical extension of modal logic ML closed under Boolean negation. Its fragments, such as modal dependence, independence, and inclusion logic, are well-understood. However, due to the unrestricted…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We study the problem of learning linear temporal logic (LTL) formulas from examples, as a first step towards expressing a property separating positive and negative instances in a way that is comprehensible for humans. In this paper we…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…