相关论文: Verifying the Unification Algorithm in LCF

We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…

Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…

We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general…

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…

In this article, the hierarchy of LFIs L$_n^k$, Logics of Controlled Consistency (LCC), is introduced. Inspired by da Costa's original C$_n$ systems, this hierarchy can represent different degrees of paraconsistent commitment and different…

We prove that the theory of the models constructible using finitely many cofinality quantifiers - $C_{\lambda_{1},...,\lambda_{n}}^{*}$ and $C_{<\lambda_{1},...,<\lambda_{n}}^{*}$ for $\lambda_{1},...,\lambda_{n}$ regular cardinals - is…

We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator,…

The rewriting system sigma is the set of rules propagating explicit substitutions in the lambda-calculus with explicit substitutions. In this note, we prove the undecidability of unification modulo sigma.

Switched systems are known to exhibit subtle (in)stability behaviors requiring system designers to carefully analyze the stability of closed-loop systems that arise from their proposed switching control laws. This paper presents a formal…

We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…

Suppose we have been sold on the idea that formalised proofs in an LCF system should resemble their written counterparts, and so consist of formulas that only provide signposts for a fully verified proof. To be practical, most of the fully…

I explain a direct approach to differentiation and integration. Instead of relying on the general notions of real numbers, limits and continuity, we treat functions as the primary objects of our theory, and view differentiation as division…

We study LFD, a base logic of functional dependence introduced by Baltag and van Benthem (2021) and its connections with the guarded fragment GF of first-order logic. Like other logics of dependence, the semantics of LFD uses teams: sets of…

We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…

For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…

The relationship between Lexical-Functional Grammar (LFG) {\em functional structures} (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that correctly explains…

We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…

We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…