Related papers: Synthetic Tait Computability the Hard Way

Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require…

We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…

In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications.…

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…

Let P be any pure type system, we are going to show how we can extend P into a PTS P' which will be used as a proof system whose formulas express properties about sets of terms of P. We will show that P' is strongly normalizable if and only…

We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of…

I consider the following generic scenario: an abstract model M of some 'real' system is only partially presented, or partially known to us, and we have to ensure that the actual system satisfies a given specification, formalised in some…

We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…

Let A be a finite subset of the natural numbers containing 0, and let f(n) denote the number of ways to write n in the form $\sum e_j2^j$, where $\e_j \in A$. We show that there exists a computable T = T(A) so that the sequence (f(n) mod 2)…

Our objective in this note is to comment briefly on the newly emerging literature on computer-aided proofs in Social Choice Theory. We shall specifically comment on two papers, one by Tang and Lin (2009) and another by Geist and Endriss…

We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…

This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…

This paper describes the celebrated aperiodic hat tiling by Smith et al. [Comb. Theory 8 (2024), 6] as generated by an overlapping iterated function system. We briefly introduce and study infinite sequences of iterated function systems that…

Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…

Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…

This paper develops a critical theory of artificial intelligence, within a historical constellation where computational systems increasingly generate cultural content that destabilises traditional distinctions between human and machine…

We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with $\eta$-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one level process…