Related papers: The logic of interactive Turing reduction
The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
Interpretable representations are the backbone of many explainers that target black-box predictive systems based on artificial intelligence and machine learning algorithms. They translate the low-level data representation necessary for good…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
While previous sentiment analysis research has concentrated on the interpretation of explicitly stated opinions and attitudes, this work initiates the computational study of a type of opinion implicature (i.e., opinion-oriented inference)…
We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…
We discuss the legacy of Alan Turing and his impact on computability and analysis.
In this paper we present an introduction to the area of computability in dynamical systems. This is a fairly new field which has received quite some attention in recent years. One of the central questions in this area is if relevant…
The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to…
Alan Turing's pioneering work on computability, and his ideas on morphological computing support Andrew Hodges' view of Turing as a natural philosopher. Turing's natural philosophy differs importantly from Galileo's view that the book of…
We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…