Related papers: Expressiveness and Completeness in Abstraction
We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state…
The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…
We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it in models from that class. Rational Kripke models are based on (generally infinite) rational graphs,…
The most prominent formal criterion for secure compilation is full abstraction, the preservation and reflection of contextual equivalence. Recent work introduced robust compilation, defined as the preservation of robust satisfaction of…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
Let ML(U^+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the relative definability of ML(U^+) relative to finite transitive frames in the…
We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…
We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world,…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
We consider various notions of completeness in symplectic topology and ask two related questions. Does a complete open symplectic manifold remain complete after excising a subset? Can two sets be made arbitrarily far apart by adjusting the…
The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…