Related papers: Feasible constructivism
Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. We study the problem of how multiple such judgments can be aggregated. We define the…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…
This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…
We investigate the complexity of explicit construction problems, where the goal is to produce a particular object of size $n$ possessing some pseudorandom property in time polynomial in $n$. We give overwhelming evidence that $\bf{APEPP}$,…
This is an expository paper about the Borel complexity of structure and classification theorems. It sorts several classical problems relative to known benchmarks of complexity. As a corollary various problems proposed by people such as von…
We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding…
To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…
Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…