The Law of Evidence and Labelled Deduction: Ten Years Later

in Journal of Applied Logic (2022), 9(4), 887-956

The purpose of this position paper is to reveal, through examples, the potential for collaboration between the theory of legal reasoning on the one hand, and some recently developed instruments of formal ... [more ▼]

The purpose of this position paper is to reveal, through examples, the potential for collaboration between the theory of legal reasoning on the one hand, and some recently developed instruments of formal logic. Three zones of contact are highlighted. 1. The law of evidence, in the light of labelled deductive systems (LDSs), discussed through the example of the admissibility of hearsay evidence. 2. The give and take of legal debate in general, and regarding the acceptability of evidence in particular, represented using the abstract systems of argumentation developed in logic, notably the coloured graphs of BenchCapon. This is considered through an imaginary example. 3. The use of Bayesian networks as tools for analysing the effects of uncertainty on the legal status of actions, illustrated via the same example These three kinds of technique do not exclude each other. On the contrary, many cases of legal argument will need the combined resources of all three. [less ▲]

On the Complexity of Input/Output Logic

in Journal of Applied Logic (2017)

A neural cognitive model of argumentation with application to legal inference and decision making

in Journal of Applied Logic (2014), 12(2), 109--127

Propositional Dynamic Logic for Searching Games with Errors

in Journal of Applied Logic (2014), 12(4), 377-394

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+1-valued Kripke models and a corresponding language based on a modal extension ... [more ▼]

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+1-valued Kripke models and a corresponding language based on a modal extension of Łukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the Rényi - Ulam searching game with errors. Our main result is the axiomatization of the theory of the n+1-valued Kripke models. This result is obtained through filtration of the canonical model of the smallest n+1-valued propositional dynamic logic. [less ▲]

Future determination of entities in Talmudic public announcement logic

in Journal of Applied Logic (2013), 11(1), 63--90

Substantive and procedural norms in normative multiagent systems

in Journal of Applied Logic (2008), 6(2), 152171

Procedural norms are instrumental norms addressed to agents playing a role in the normative system, for example to motivate these role playing agents to recognize violations or to apply sanctions ... [more ▼]

Procedural norms are instrumental norms addressed to agents playing a role in the normative system, for example to motivate these role playing agents to recognize violations or to apply sanctions. Procedural norms have first been discussed in law, where they address legal practitioners such as legislators, lawyers and policemen, but they are discussed now too in normative multiagent systems to motivate software agents. Procedural norms aim to achieve the social order specified using regulative norms like obligations and permissions, and constitutive norms like counts-as obligations. In this paper we formalize procedural, regulative and constitutive norms using input/output logic enriched with an agent ontology and an abstraction hierarchy. We show how our formalization explains Castelfranchi's notion of mutual empowerment, stating that not only the agents playing a role in a normative system are empowered by the normative system, but the normative system itself is also empowered by the agents playing a role in it. In our terminology, the agents are not only institutionally empowered, but they are also delegated normative goals from the system. Together, institutional empowerment and normative goal delegation constitute a mechanism which we call delegation of power, where agents acting on behalf of the normative system become in charge of recognizing which institutional facts follow from brute facts. [less ▲]