On a Partial Decision Method for Dynamic Proofs

This paper concerns a goal directed proof procedure for the propositional fragment of the adaptive logic ACLuN1. At the propositional level, it forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.Comment: 18 pages. Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

Avoiding deontic explosion by contextually restricting aggregation

In this paper, we present an adaptive logic for deontic conflicts, called P2.1(r), that is based on Goble's logic SDLaPe-a bimodal extension of Goble's logic P that invalidates aggregation for all prima facie obligations. The logic P2.1(r) has several advantages with respect to SDLaPe. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation "as much as possible". It thus leads to a richer consequence set than SDLaPe. The logic P2.1(r) avoids Goble's criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the 'toy examples' from the literature as well as more complex ones

Logics for qualitative inductive generalization

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics

Model Checking Spatial Logics for Closure Spaces

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool

Specifying and Verifying Properties of Space - Extended Version

The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems distributed in physical space. Traditional verification techniques are well suited to analyse the temporal evolution of programs; properties of space are typically not explicitly taken into account. We propose a methodology to verify properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to a more general setting, also encompassing discrete, graph-based structures. We further extend the framework with a spatial until operator, and define an efficient model checking procedure, implemented in a proof-of-concept tool.Comment: Presented at "Theoretical Computer Science" 2014, Rom