计算机科学中的逻辑

The goal of this contribution is to provide worksheets in Coq for students to learn about divisibility and binomials. These basic topics are a good case study as they are widely taught in the early academic years (or before in France). We…

Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…

In the impredicative type theory of System F ({\lambda}2), it is possible to create inductive data types, such as natural numbers and lists. It is also possible to create coinductive data types such as streams. They work well in the sense…

We present a formal theory for analysing causality in cyber-physical systems. To this end, we extend the theory of actual causality by Halpern and Pearl to cope with the continuous nature of cyber-physical systems. Based on our theory, we…

We report on our journey to develop ProofBuddy, a web application that is powered by a server-side instance of the proof assistant Isabelle, for the teaching and learning of proofs and proving. The journey started from an attempt to use…

The importance of category theory in recent developments in both mathematics and in computer science cannot be overstated. However, its abstract nature makes it difficult to understand at first. Graphical languages have been developed to…

In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…

This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…

Bigraphical Reactive Systems (BRSs) are a graph-rewriting formalism describing systems evolving in two dimensions: spatially, e.g. a person in a room, and non-spatially, e.g. mobile phones communicating regardless of location. Despite use…

We present a computationally grounded semantics for counterfactual conditionals in which i) the state in a model is decomposed into two elements: a propositional valuation and a causal base in propositional form that represents the causal…

Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics…

We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…

The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…

This paper studies the extent to which branching-time properties can be adequately verified using runtime monitors. We depart from the classical setup where monitoring is limited to a single system execution and investigate the enhanced…

In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework,…

We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain theory (including the inductive fixed point object and the…

This paper introduces and formally verifies a novel geometric framework for first-order stochastic dominance (FSD) in $N$ dimensions using the Lean 4 theorem prover. Traditional analytical approaches to multi-dimensional stochastic…

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…

A residuated semigroup is a structure $\langle A,\le,\cdot,\backslash,/ \rangle$ where $\langle A,\le \rangle$ is a poset and $\langle A,\cdot \rangle$ is a semigroup such that the residuation law $x\cdot y\le z\iff x\le z/y\iff y\le x…

Optimization Modulo Theories (OMT) extends Satisfiability Modulo Theories (SMT) with the task of optimizing some objective function(s). In OMT solvers, a CDCL-based SMT solver enumerates theory-satisfiable total truth assignments, and a…