计算机科学中的逻辑

We introduce a dialect of the Asynchronous pi-calculus, called AWpi, in which (1) an input name may be owned, at any time, by at most one process; (2) each name has either only the input or only the output capability. As a result, special…

In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…

In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…

This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…

A key requirement on any well-behaved process language is its compositionality: behavioural equivalence of processes should be respected by the constructors of the language. Turi and Plotkin's abstract GSOS provides an elegant bialgebraic…

This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\sf…

Type systems which account for resource sensitive computations can generally be split into two styles: First, substructural logics such as Linear Logic which seek to restrict weakening and contraction and reintroduce them in a controlled…

We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers of the form $2n^3-5n+3$, etc.) Although the full attendant…

The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…

Property-Directed Reachability (PDR/IC3) is a standard workhorse for hardware safety verification, but most implementations are tuned primarily for time-to-answer and treat the produced invariant or counterexample as a secondary byproduct.…

We present a new algorithm for deciding formula entailment in orthologic (a sound approximation of classical logic) that avoids the costly preprocessing phase of prior implementations while retaining the same $\mathcal{O}(n^2(1+|A|))$…

We present a framework for verifying the deterministic structured computations surrounding a large language model rather than the model itself, extending a Lean 4 trust-boundary architecture to the generic interfaces of modern LLM…

There have recently been several developments in synthetic mathematics using extensions of dependent type theory with univalence and higher inductive types: simplicial homotopy type theory, synthetic algebraic geometry and synthetic Stone…

Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…

We introduce ocLTL, the case of LTL+P modulo {\omega}-categorical theories. We reduce its realizability and synthesis problems into the corresponding problems in propositional LTL+P. The core of the reduction replaces each data subformula…

The belief construction is a fundamental technique for transforming partially observable systems to fully observable ones while preserving the relevant semantics. It plays a central role in the analysis of partially observable systems, in…

This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.

Laminar set systems consist of non-crossing subsets of a universe with set inclusion essentially corresponding to the descendant relationship of a tree, the so-called laminar tree. Laminar set systems lie at the core of many graph…

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by…

The Brunauer--Emmett--Teller (BET) method is a standard tool for estimating surface areas from adsorption isotherms, yet practical implementations involve multiple algorithmic steps whose correctness is rarely made explicit. In this work,…