Related papers: Transordinal Fixed-Point Operators and Self-Refere…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
We provide here an epistemic analysis of arbitrary strategic games based on the possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. Our approach is based on Tarski's…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
This paper updates the cognitive model, firstly by creating two systems and then unifying them over the same structure. It represents information at the semantic level only, where labelled patterns are aggregated into a 'type-set-match'…
In this paper we revisit the regular-language representation of game semantics of second-order recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of…
The next-token prediction (NTP) objective trains language models to predict a single token at each step, even though many continuations can express the same meaning. For example, in the sentence ``this sticker can be placed here'',…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Semantic matching, which aims to determine the matching degree between two texts, is a fundamental problem for many NLP applications. Recently, deep learning approach has been applied to this problem and significant improvements have been…
Establishing correspondences between images remains a challenging task, especially under large appearance changes due to different viewpoints or intra-class variations. In this work, we introduce a strong semantic image matching learner,…
In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *--weakly convex graph and we prove some fixed point theorems for these…
Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…
SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. The recommendation only specifies semantics for non-recursive SHACL; recently, some efforts have been made to allow recursive SHACL schemas. In this…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
We propose a general framework to study language emergence through signaling games with neural agents. Using a continuous latent space, we are able to (i) train using backpropagation, (ii) show that discrete messages nonetheless naturally…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
Classical game theory treats players as special---a description of a game contains a full, explicit enumeration of all players---even though in the real world, "players" are no more fundamentally special than rocks or clouds. It isn't…
Simple reference games are of central theoretical and empirical importance in the study of situated language use. Although language provides rich, compositional truth-conditional semantics to facilitate reference, speakers and listeners may…