Related papers: Formative processes with applications to the decis…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Motivated by problems involving end extensions of models of set theory, we develop the rudiments of the power admissible cover construction (over ill-founded models of set theory), an extension of the machinery of admissible covers invented…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
We develop a constructive theory of continuous domains from the perspective of program extraction. Our goal that programs represent (provably correct) computation without witnesses of correctness is achieved by formulating correctness…
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
This paper proposes a change in perspective on the ``transformation of values'' problem: from ``searching for a single constant solution'' to ``characterizing the allocation space under objective constraints imposed by the physical…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…