计算机科学中的逻辑

Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…

In multi-agent system design, a crucial aspect is to ensure robustness, meaning that for a coalition of agents A, small violations of adversarial assumptions only lead to small violations of A's goals. In this paper we introduce a logical…

Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…

The TARK conference (Theoretical Aspects of Rationality and Knowledge) is a conference that aims to bring together researchers from a wide variety of fields, including computer science, artificial intelligence, game theory, decision theory,…

Minimal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped, whatever the update mode. They correspond to the attractors of the most permissive mode. Due to their versatility, the computation of MTSs has recently…

In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…

There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…

Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost…

We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to disprove termination of transition systems, and we evaluate its…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…

We study the problem of $P$-interpolation, where $P$ is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the $P$-interpolating terms, we use a hierarchic approach: This allows us to…

We present a compositional model checking algorithm for Markov decision processes, in which they are composed in the categorical graphical language of string diagrams. The algorithm computes optimal expected rewards. Our theoretical…

This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (gbts) and a new, generalized variant,…

We show that adding recursion does not increase the total functions definable in the typed $\lambda\beta\eta$-calculus or the partial functions definable in the $\lambda\Omega$-calculus. As a consequence, adding recursion does not increase…

We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible…

We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…

We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the…

This paper studies the problem of model-checking of probabilistic automaton and probabilistic one-counter automata against probabilistic branching-time temporal logics (PCTL and PCTL$^*$). We show that it is undecidable for these problems.…

In a recent letter [Information Processing Letters~104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. This paper provides some alternative and simple characterizations for the…