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Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…

Structural subtyping and parametric polymorphism provide similar flexibility and reusability to programmers. For example, both features enable the programmer to provide a wider record as an argument to a function that expects a narrower…

Tabled evaluation is an implementation technique that solves some problems of traditional Prolog systems in dealing with recursion and redundant computations. Most tabling engines determine if a tabled subgoal will produce or consume…

Large language models have been proven to be capable of handling complex linguistic and cognitive tasks. Therefore their usage has been extended to tasks requiring logical reasoning ability such as Mathematics. In this paper, we propose a…

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…

Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…

2. In Section 3, we used some vague statements to affirm the training process of the neural network, which cannot support others to reproduce the results of the paper. In addition, this section does not show the difference between this…

Latent reasoning via continuous chain-of-thoughts (Latent CoT) has emerged as a promising alternative to discrete CoT reasoning. Operating in continuous space increases expressivity and has been hypothesized to enable superposition: the…

Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…

Prototypical self-supervised learning methods consistently suffer from partial prototype collapse, where multiple prototypes converge to nearly identical representations. This undermines their central purpose -- providing diverse and…

We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…

Existing interpretation algorithms have found that, even deep models make the same and right predictions on the same image, they might rely on different sets of input features for classification. However, among these sets of features, some…

Deep neural networks have achieved remarkable performance in various text-based tasks but often lack interpretability, making them less suitable for applications where transparency is critical. To address this, we propose ProtoLens, a novel…

Existing self-supervised learning methods learn representation by means of pretext tasks which are either (1) discriminating that explicitly specify which features should be separated or (2) aligning that precisely indicate which features…

The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…

The $\lambda$$\Pi$-calculus modulo theory is a logical framework in which various logics and type systems can be encoded, thus helping the cross-verification and interoperability of proof systems based on those logics and type systems. In…