Related papers: Metric Structures and Probabilistic Computation

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…

We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a…

One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…

In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.

This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…

Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…

Existing decision-theoretic reasoning frameworks such as decision networks use simple data structures and processes. However, decisions are often made based on complex data structures, such as social networks and protein sequences, and rich…