计算机科学中的逻辑

The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…

This paper introduces a framework for assisting policy authors in refining and improving their policies. In particular, we focus on authorization and obligation policies that can be encoded in Gelfond and Lobo's AOPL language for policy…

We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness…

This volume contains the papers presented at LN2FR 2022: The International Workshop on Methodologies for Translating Legal Norms into Formal Representations, held on December 14, 2022 in association with 35th International Conference on…

We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an important 19th century result that motivated the development…

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

In [4], we introduced an extension of team semantics (causal teams) which assigns an interpretation to interventionist counterfactuals and causal notions based on them (as e.g. in Pearl's and Woodward's manipulationist approaches to…

We study the complexity of the problem of training neural networks defined via various activation functions. The training problem is known to be existsR-complete with respect to linear activation functions and the ReLU activation function.…

We present a generic tree-interpolation algorithm in the SMT context with quantifiers. The algorithm takes a proof of unsatisfiability using resolution and quantifier instantiation and computes interpolants (which may contain quantifiers).…

We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…

Working in a semi-constructive logical system that supports the extraction of concurrent programs, we extract a program inverting non-singular real valued matrices from a constructive proof based on Gaussian elimination. Concurrency is used…

We present CureSpec, the first model-checking based framework for automatic repair of programs with respect to information leaks in the presence of side-channels and speculative execution. CureSpec is based on formal models of attacker…

If the sequent (Gamma entails forall x exists y A) is provable in first order constructive natural deduction, then the theory (Gamma, forall x (f (x)/y)A), where f is a new function symbol, is a conservative extension of Gamma.

Given a first-order theory and a proof that it is consistent, can we design a proof-search method for this theory that fails in finite time when it attempts to prove the formula False?

Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…

In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…

We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show…

Elliptic curves are fundamental objects in number theory and algebraic geometry, whose points over a field form an abelian group under a geometric addition law. Any elliptic curve over a field admits a Weierstrass model, but prior formal…

Technology advances give us the hope of driving without human error, reducing vehicle emissions and simplifying an everyday task with the future of self-driving cars. Making sure these vehicles are safe is very important to the continuation…

Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…