计算机科学中的逻辑

It is well known that the length of a beta-reduction sequence of a simply typed lambda-term of order k can be huge; it is as large as k-fold exponential in the size of the lambda-term in the worst case. We consider the following relevant…

Event Structures (ESs) address the representation of direct relationships between individual events, usually capturing the notions of causality and conflict. Up to now, such relationships have been static, i.e., they cannot change during a…

In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…

We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and…

We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct.

We investigate the interplay between a modality for controlling the behaviour of recursive functional programs on infinite structures which are completely silent in the syntax. The latter means that programs do not contain "marks" showing…

A cyclic proof system, called CLKID-omega, gives us another way of representing inductive definitions and efficient proof search. The 2005 paper by Brotherston showed that the provability of CLKID-omega includes the provability of LKID,…

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain…

In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes…

In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that…

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with…

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove…

Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi…

The homotopical approach to intensional type theory views proofs of equality as paths. We explore what is required of an object $I$ in a topos to give such a path-based model of type theory in which paths are just functions with domain $I$.…

The inhabitation problem for intersection types in the lambda-calculus is known to be undecidable. We study the problem in the case of non-idempotent intersection, considering several type assignment systems, which characterize the solvable…

We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…

As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the…

Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…

This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard…

Many reasoning problems are based on the problem of satisfiability (SAT). While SAT itself becomes easy when restricting the structure of the formulas in a certain way, the situation is more opaque for more involved decision problems. We…