Introducing reactive Kripke semantics and arc accessibility

in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 7-53

Ordinary Kripke models are not reactive. When we evaluate (test/ measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This ... [more ▼]

Ordinary Kripke models are not reactive. When we evaluate (test/ measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. The additional device we add to Kripke semantics to make it reactive is to allow the accessibility relation to access itself. Thus the accessibility relation R of a reactive Kripke model contains not only pairs (a,b)∈R of possible worlds (b is accessible to a, i.e., there is an accessibility arc from a to b) but also pairs of the form (t ,(a,b))∈R, meaning that the arc (a,b) is accessible to t, or even connections of the form((a,b),(c,d))∈R. This new kind of Kripke semantics allows us to characterise more axiomatic modal logics (with one modality) by a class of reactive frames. There are logics which cannot be characterised by ordinary frames but which can be characterised by reactive frames. We also discuss the manifestation of the ‘reactive’ idea in the context of automata theory, where we allow the automaton to react and change it’s own definition as it responds to input, and in graph theory, where the graph can change under us as we manipulate it. [less ▲]

Introducing reactive modal tableaux

in Annals of Mathematics & Artificial Intelligence (2012), 66(1-4), 55-79

This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the ... [more ▼]

This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the possibility of transitions moving from one state to another, we can naturally imagine a path beginning at an initial state and moving along the path following allowed transitions. If our starting point is s0, and the path is s0,s1,...,sn, then the system is ordinary non-reactive system if the options available at sn (i.e., which states t we can go to from sn) do not depend on the path s0,...,sn (i.e., do not depend on how we got to sn). Otherwise if there is such dependence then the system is reactive. It seems that the simple idea of taking existing systems and turning them reactive in certain ways, has many new applications. The purpose of this paper is to introduce reactive tableaux in particular and illustrate and present some of the applications of reactivity in general. Mathematically one can take a reactive system and turn it into an ordinary system by taking the paths as our new states. This is true but from the point of view of applications there is serious loss of information here as the applicability of the reactive system comes from the way the change occurs along the path. In any specific application, the states have meaning, the transitions have meaning and the paths have meaning. Therefore the changes in the system as we go along a path can have very important meaning in the context, which enhances the usability of the model. [less ▲]

What Is Negation as Failure?

in Logic Programs, Norms and Action - Essays in Honor of Marek J. Sergot on the Occasion of His 60th Birthday (2012)

Bipolar Argumentation Frames and Contrary to Duty Obligations, Preliminary Report

in Computational Logic in Multi-Agent Systems - 13th International Workshop CLIMA XIII, Montpellier, France, August 27-28, 2012. Proceedings (2012)

Conditionals and Modularity in General Logics

Book published by Springer (2011)

Introducing Equational Semantics for Argumentation Networks

in ECSQARU (2011)

This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations ... [more ▼]

This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, etc, etc. The equational approach has its conceptual roots in the 19th century following the algebraic equational approach to logic by George Boole, Louis Couturat and Ernst Schroeder. [less ▲]

Reactive automata

in Information and Computation (2011), 209(4), 692704

A reactive automaton has extra links whose role is to change the behaviour of the automaton. We show that these links do not increase the expressiveness of finite automata but that they can be used to ... [more ▼]

A reactive automaton has extra links whose role is to change the behaviour of the automaton. We show that these links do not increase the expressiveness of finite automata but that they can be used to reduce dramatically their state number both in the deterministic case and the non-deterministic case. Typical examples of regular expressions associated with deterministic automata of ex- ponential size according to the length of the expression show that reactive links provide an alternative representation of total linear size for the language [less ▲]

Argumentative Agents Negotiating on Potential Attacks

in KES-AMSTA (2011)

When arguing, agents may want to discuss about the details after agreeing about the general problems. We propose to model this kind of situation using an extended argumentation framework with potential ... [more ▼]

When arguing, agents may want to discuss about the details after agreeing about the general problems. We propose to model this kind of situation using an extended argumentation framework with potential attacks. Agents negotiation about raising potential attacks or not, in order to maximize the number of their accepted arguments. The result of the negotiation process consists in the formation of coalitions composed by those agents which have found an agreement. The two proposed negotiation protocols have been implemented and an evaluation, addressed by means of experimental results, shows which combination of strategies and negotiation protocol allows the agents to optimize outcomes. [less ▲]

Coalition Formation via Negotiation in Multiagent Systems with Voluntary Attacks

in Proceedings of the 22th Belgian-Netherlands Conference on Artificial Intelligence (BNAIC'10) (2010)

Argumentation networks are put forward by Dung considering only one kind of attack among argu- ments. In this paper, we propose to extend Dung’s argumentation framework with voluntary attacks in the ... [more ▼]

Argumentation networks are put forward by Dung considering only one kind of attack among argu- ments. In this paper, we propose to extend Dung’s argumentation framework with voluntary attacks in the context of multiagent systems, characterized by the possibility of the attacker to decide whether to attack or not. Enabling voluntary attacks impacts on the acceptability of the arguments in the framework, and therefore it becomes subject of debate between the agents. Agents can negotiate about which subset of voluntary attacks can be raised, and they form coalitions after the negotiation process. [less ▲]

A Theory of Hierarchical Consequence and Conditionals

in Journal of Logic, Language and Information (2010), 19(1), 332

We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked ... [more ▼]

We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall A-ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved. [less ▲]