Related papers: The Grail theorem prover: Type theory for syntax a…

We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…

The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…

Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…

A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…

We present an approach for modeling the Semantic Web as a type system. By using a type system, we can use symbolic representation for representing linked data. Objects with only data properties and references to external resources are…

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…

Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant…

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…

Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…

Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…

In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…

Graph-matching metrics such as Smatch are the de facto standard for evaluating neural semantic parsers, yet they capture surface overlap rather than logical equivalence. We reassess evaluation by pairing graph-matching with automated…

We present a simple programming language based on G\"odel numbering and prime factorization, enhanced with explicit, scoped loops, allowing for easy program composition. Further, we will present a theorem prover that allows expressing and…

Proof Theory and Type Theory are two branches of mathematical logic and theoretical computer science that explore the structure of mathematical proofs and the foundations of computation. Both are crucial for understanding formal systems,…

Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…