Fernando R. Velázquez-Quesada

Inference and update

We look at two fundamental logical processes, often intertwined in planning and problem solving: inference and update. Inference is an internal process with which we uncover what is implicit in the information we already have. Update, on the other hand, is produced by external communication, usually in the form of announcements and in general in the form of observations, giving us information that might not have been available (even implicitly) before. Both processes have received attention from the logic community, usually separately. In this work, we develop a logical language that allows us to describe them together. We present syntax, semantics and a complete axiom system; we discuss similarities and differences with other approaches and mention how the work can be extended.

The dynamics of awareness

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference—and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we use a static base from the existing awareness literature, extending it into a dynamic system that includes traditional acts of observation, but also adding and dropping formulas from the current ‘awareness’ set. We give a completeness theorem, and we show how this dynamics updates explicit knowledge. Then we extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. Our contribution can be seen as a ‘dynamification’ of existing awareness logics.

Twelve angry men: a study on the fine-grain of announcements

By moving from a suggestive example, the paper analyzes how information flows among agents involved in a deliberation. By deliberating, agents become aware of details, draw the attention of the group to some issues, perform inferences and announce what they know. The proposed framework--which builds on the paradigm of dynamic logic-- captures how, during a deliberation, information results from stepwise multi-agent interaction.

Dynamic Epistemic Logic for Implicit and Explicit Beliefs

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs.

Learning and teaching as a game: a sabotage approach

In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teachers abilities and strategies is in fact undeniable. Motivated by this observation, this paper highlights the interactive nature of learning by showing its relation with games. We show how learning can be seen as a sabotage-type game between Teacher and Learner, and we present different variants based on the level of cooperativeness and the actions available to the players, characterizing the existence of winning strategies by formulas of Sabotage Modal Logic and analyzing their complexity. We also give a two-way conceptual account of how to further combine games and learning: we propose to use game theory to analyze the grammar inference approach, and moreover, we indicate that existing inductive inference games can be analyzed using learning theory tools. Our work aims at unifying game-theoretical and logical approach to formal learning theory.

An epistemic and dynamic approach to abductive reasoning: Abductive problem and abductive solution

Abstract We propose a study of abductive reasoning addressing it as an epistemic process that involves both an agentʼs information and the actions that modify this information. More precisely, we present and discuss definitions of an abductive problem and an abductive solution in terms of an agentʼs information, that is, in terms of knowledge and beliefs. The discussion is then formalised by ‘implementing’ our definitions in a dynamic epistemic logic framework, where the properties of these definitions are studied, an epistemic action that represents the application of an abductive step is introduced, and an illustrative example is provided. A number of the most interesting properties of abductive reasoning (those highlighted by Peirce) are shown to be better modelled within this approach.

A Note on Reliability-Based Preference Dynamics

This paper continues a line of work that studies individual preference upgrades in order to model situations akin to a process of public deliberation in collective decision making. It proposes a general upgrade policy, presenting its semantic definition and a corresponding modality for describing its effects as well as a complete axiom system.

Generation and Selection of Abductive Explanations for Non-Omniscient Agents

Among the non-monotonic reasoning processes, abduction is one of the most important. Usually described as the process of looking for explanations, it has been recognized as one of the most commonly used in our daily activities. Still, the traditional definitions of an abductive problem and an abductive solution mention only theories and formulas, leaving agency out of the picture. Our work proposes a study of abductive reasoning from an epistemic and dynamic perspective. In the first part we explore syntactic definitions of both an abductive problem in terms of an agent’s information and an abductive solution in terms of the actions that modify the agent’s information. We look at diverse kinds of agents, including not only omniscient ones but also those whose information is not closed under logical consequence and those whose reasoning abilities are not complete. In the second part, we look at an existing logical framework whose semantic model allows us to interpret the previously stated formulas, and we define two actions that represent forms of abductive reasoning.

Dynamic logics for explicit and implicit information

Classical Epistemic Logic (EL) is a compact and powerful framework for representing an agent’s information. In its dynamic versions (Dynamic Epistemic Logic), it also describes the information flow driven by observation and communication. Nevertheless, it makes a strong idealization: the agent’s information is closed under logical consequence, making truth-preserving inference uninformative. This criticism extends to its dynamics versions: acts of observation and communication provides the agent not only with the new information but also with all logical consequences of it. Thus, dynamic epistemic logics lack of an account of the step-by-step information flow driven by agent’s inferences, a concern that arises not only in epistemic contexts, but also in doxastic areas. The extended version of the present abstract [1] combines ideas from the earlier literature proposing a unified framework to address these problems.

How to make friends: A logical approach to social group creation

This paper studies the logical features of social group creation. We focus on the mechanisms which indicate when agents can form a team based on the correspondence in their set of features (behavior, opinions, etc.). Our basic approach uses a semi-metric on the set of agents, which is used to construct a network topology. Then it is extended with epistemic features to represent the agents’ epistemic states, allowing us to explore group-creation alternatives where what matters is not only the agent’s differences but also what they know about them. We use tools of dynamic epistemic logic to study the properties of different strategies to network formations.