Related papers: The Delta-framework
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
In paper describes the new logic programming language Delta, which have a many good properties. Delta-programs is p-computable, verifiable and can translation on other languages. Also we describe the Delta-methodology for constructing…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of definitional equality are based on a confluent,…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the…
We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
This paper proposes X2-DFD, an eXplainable and eXtendable framework based on multimodal large-language models (MLLMs) for deepfake detection, consisting of three key stages. The first stage, Model Feature Assessment, systematically…
The concurrent logical framework CLF is an extension of the logical framework LF designed to specify concurrent and distributed languages. While it can be used to define a variety of formalisms, reasoning about such languages within CLF has…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
We reflect on programming with complicated effects, recalling an undeservingly forgotten alternative to monadic programming and checking to see how well it can actually work in modern functional languages. We adopt and argue the position of…
The unified correspondence theory for distributive lattice expansion logics (DLE-logics) is specialized to strict implication logics. As a consequence of a general semantic consevativity result, a wide range of strict implication logics can…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…