Related papers: Definability and Interpolation in Philosophy
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
The paper investigates properties of the conditional independence relation between pieces of information. This relation is also known in the database theory as embedded multivalued dependency. In 1980, Parker and Parsaye-Ghomi established…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is…
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…
A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By…
Interpretability logics are endowed with relational semantics \`a la Kripke: Veltman semantics. For certain applications though, this semantics is not fine-grained enough. Back in 1992, in the research group of de Jongh, the notion of…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…
Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
Our paper investigates the linear logic of knowledge and time LTK_r with reflexive intransitive time relation. The logic is defined semantically, -- as the set of formulas which are true at special frames with intransitive and reflexive…
There are investigated the generalized methods of cognition of the Existing, i.e. everything that is able to influence to the cognizer, and everything differed from the Existing is postulated as indistinguishable from the non-existing and…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…