Related papers: Tuple Interpretations for Higher-Order Rewriting
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…
Deep learning techniques are increasingly popular in the textual entailment task, overcoming the fragility of traditional discrete models with hard alignments and logics. In particular, the recently proposed attention models (Rockt\"aschel…
We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions…
Logically constrained term rewriting systems (LCTRSs) are a program analyzing formalism with native support for data types which are not (co)inductively defined. As a first-order formalism, LCTRSs have accommodated only analysis of…
We present a Bounded Model Checking technique for higher-order programs. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
Matrix interpretations generalize linear polynomial interpretations and have been proved useful in the implementation of tools for automatically proving termination of Term Rewriting Systems. In view of the successful use of rational…
Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…
There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
Most recent work on interpretability of complex machine learning models has focused on estimating $\textit{a posteriori}$ explanations for previously trained models around specific predictions. $\textit{Self-explaining}$ models where…
In standard methodology for natural language processing, entities in text are typically embedded in dense vector spaces with pre-trained models. The embeddings produced this way are effective when fed into downstream models, but they…
Researchers have relegated natural language processing tasks to Transformer-type models, particularly generative models, because these models exhibit high versatility when performing generation and classification tasks. As the size of these…
Transformers are widely used in natural language processing, where they consistently achieve state-of-the-art performance. This is mainly due to their attention-based architecture, which allows them to model rich linguistic relations…
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect…