Lluís Godo

TARK Conference 2025 Conference Paper

Conditionals Based on Selection Functions, Modal Operators and Probabilities

• Tommaso Flaminio
• Lluís Godo
• Giuliano Rosella

Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.

JELIA Conference 2021 Conference Paper

Probabilistic Argumentation: An Approach Based on Conditional Probability -A Preliminary Report-

• Pilar Dellunde
• Lluís Godo
• Amanda Vidal

Abstract A basic form of an instantiated argument is as a pair (support, conclusion) standing for a conditional relation ‘if support then conclusion’. When this relation is not fully conclusive, a natural choice is to model the argument strength with the conditional probability of the conclusion given the support. In this paper, using a very simple language with conditionals, we explore a framework for probabilistic logic-based argumentation based on an extensive use of conditional probability, where uncertain and possibly inconsistent domain knowledge about a given scenario is represented as a set of defeasible rules quantified with conditional probabilities. We then discuss corresponding notions of attack and defeat relations between arguments, providing a basis for appropriate acceptability semantics, e. g. based on extensions or on DeLP-style dialogical trees.

JAIR Journal 2017 Journal Article

Managing Different Sources of Uncertainty in a BDI Framework in a Principled Way with Tractable Fragments

• Kim Bauters
• Kevin McAreavey
• Weiru Liu
• Jun Hong
• Lluís Godo
• Carles Sierra

The Belief-Desire-Intention (BDI) architecture is a practical approach for modelling large-scale intelligent systems. In the BDI setting, a complex system is represented as a network of interacting agents - or components - each one modelled based on its beliefs, desires and intentions. However, current BDI implementations are not well-suited for modelling more realistic intelligent systems which operate in environments pervaded by different types of uncertainty. Furthermore, existing approaches for dealing with uncertainty typically do not offer syntactical or tractable ways of reasoning about uncertainty. This complicates their integration with BDI implementations, which heavily rely on fast and reactive decisions. In this paper, we advance the state-of-the-art w.r.t. handling different types of uncertainty in BDI agents. The contributions of this paper are, first, a new way of modelling the beliefs of an agent as a set of epistemic states. Each epistemic state can use a distinct underlying uncertainty theory and revision strategy, and commensurability between epistemic states is achieved through a stratification approach. Second, we present a novel syntactic approach to revising beliefs given unreliable input. We prove that this syntactic approach agrees with the semantic definition, and we identify expressive fragments that are particularly useful for resource-bounded agents. Third, we introduce full operational semantics that extend CAN, a popular semantics for BDI, to establish how reasoning about uncertainty can be tightly integrated into the BDI framework. Fourth, we provide comprehensive experimental results to highlight the usefulness and feasibility of our approach, and explain how the generic epistemic state can be instantiated into various representations.

UAI Conference 2014 Conference Paper

CAN(PLAN)+: Extending the Operational Semantics of the BDI Architecture to deal with Uncertain Information

• Kim Bauters
• Weiru Liu
• Jun Hong 0001
• Carles Sierra
• Lluís Godo

The BDI architecture, where agents are modelled based on their beliefs, desires and intentions, provides a practical approach to develop large scale systems. However, it is not well suited to model complex Supervisory Control And Data Acquisition (SCADA) systems pervaded by uncertainty. In this paper we address this issue by extending the operational semantics of CAN(PLAN) into CAN(PLAN)+. We start by modelling the beliefs of an agent as a set of epistemic states where each state, possibly using a different representation, models part of the agent’s beliefs. These epistemic states are stratified to make them commensurable and to reason about the uncertain beliefs of the agent. The syntax and semantics of a BDI agent are extended accordingly and we identify fragments with computationally efficient semantics. Finally, we examine how primitive actions are affected by uncertainty and we define an appropriate form of lookahead planning.

EUMAS Conference 2013 Conference Paper

Logics for Non-Cooperative Games with Expectations

• Lluís Godo
• Enrico Marchioni

AIJ Journal 2012 Journal Article

A defeasible reasoning model of inductive concept learning from examples and communication

• Santiago Ontañón
• Pilar Dellunde
• Lluís Godo
• Enric Plaza

This paper introduces a logical model of inductive generalization, and specifically of the machine learning task of inductive concept learning (ICL). We argue that some inductive processes, like ICL, can be seen as a form of defeasible reasoning. We define a consequence relation characterizing which hypotheses can be induced from given sets of examples, and study its properties, showing they correspond to a rather well-behaved non-monotonic logic. We will also show that with the addition of a preference relation on inductive theories we can characterize the inductive bias of ICL algorithms. The second part of the paper shows how this logical characterization of inductive generalization can be integrated with another form of non-monotonic reasoning (argumentation), to define a model of multiagent ICL. This integration allows two or more agents to learn, in a consistent way, both from induction and from arguments used in the communication between them. We show that the inductive theories achieved by multiagent induction plus argumentation are sound, i. e. they are precisely the same as the inductive theories built by a single agent with all data.

JELIA Conference 2012 Conference Paper

Extending a Temporal Defeasible Argumentation Framework with Possibilistic Weights

• Lluís Godo
• Enrico Marchioni
• Pere Pardo

Abstract Recently, a temporal extension of the argumentation defeasible reasoning system \(\mbox{\textsf{DeLP}}\) has been proposed. This system, called \(\mbox{\textsf{t-DeLP}}\), allows to reason defeasibly about changes and persistence over time but does not offer the possibility of ranking defeasible rules according to criteria of preference or certainty (in the sense of belief). In this contribution we extend \(\mbox{\textsf{t-DeLP}}\) by allowing to attach uncertainty weights to defeasible temporal rules and hence stratifying the set of defeasible rules in a program. Technically speaking, weights are modelled as necessity degrees within the frame of possibility theory, a qualitative model of uncertainty.

AIJ Journal 2011 Journal Article

A graded BDI agent model to represent and reason about preferences

• Ana Casali
• Lluís Godo
• Carles Sierra

In this research note, we introduce a graded BDI agent development framework, g-BDI for short, that allows to build agents as multi-context systems that reason about three fundamental and graded mental attitudes (i. e. beliefs, desires and intentions). We propose a sound and complete logical framework for them and some logical extensions to accommodate slightly different views on desires.

KR Conference 2008 Conference Paper

A Logical Framework to Represent and Reason about Graded Preferences and Intentions

• Ana Casali
• Lluís Godo
• Carles Sierra

In intentional agents, actions are derived from the mental attitudes and their relationships. In particular, preferences (positive desires) and restrictions (negative desires) are important proactive attitudes which guide agents to intentions and eventually to actions. In this paper, we present a general logical framework to represent and reasoning about gradual notions of desires and intentions, including sound and complete axiomatizations. Some extensions are proposed corresponding to certain additional constraints that the agent can set about the kind of preferences she is dealing with. We also show that the framework is expressive enough to describe how desires, together with other information, can lead agents to intentions.

AIJ Journal 2007 Journal Article

Negotiating using rewards

• Sarvapali D. Ramchurn
• Carles Sierra
• Lluís Godo
• Nicholas R. Jennings

Negotiation is a fundamental interaction mechanism in multi-agent systems because it allows self-interested agents to come to mutually beneficial agreements and partition resources efficiently and effectively. Now, in many situations, the agents need to negotiate with one another many times and so developing strategies that are effective over repeated interactions is an important challenge. Against this background, a growing body of work has examined the use of Persuasive Negotiation (PN), which involves negotiating using rhetorical arguments (such as threats, rewards, or appeals), in trying to convince an opponent to accept a given offer. Such mechanisms are especially suited to repeated encounters because they allow agents to influence the outcomes of future negotiations, while negotiating a deal in the present one, with the aim of producing results that are beneficial to both parties. To this end, in this paper, we develop a comprehensive PN mechanism for repeated interactions that makes use of rewards that can be asked for or given to. Our mechanism consists of two parts. First, a novel protocol that structures the interaction by capturing the commitments that agents incur when using rewards. Second, a new reward generation algorithm that constructs promises of rewards in future interactions as a means of permitting agents to reach better agreements, in a shorter time, in the present encounter. We then go on to develop a specific negotiation tactic, based on this reward generation algorithm, and show that it can achieve significantly better outcomes than existing benchmark tactics that do not use such inducements. Specifically, we show, via empirical evaluation in a Multi-Move Prisoners' Dilemma setting, that our tactic can lead to a 26% improvement in the utility of deals that are made and that 21 times fewer messages need to be exchanged in order to achieve this.

EUMAS Conference 2005 Conference Paper

Expansion Operators for Modelling Agent Reasoning in Possibilistic Defeasible Logic Programming

• Carlos Iván Chesñevar
• Guillermo Ricardo Simari
• Lluís Godo
• Teresa Alsinet

JELIA Conference 2004 Conference Paper

A Logic for Reasoning About Coherent Conditional Probability: A Modal Fuzzy Logic Approach

• Enrico Marchioni
• Lluís Godo

Abstract In this paper we define a logic to reason about coherent conditional probability, in the sense of de Finetti. Under this view, a conditional probability μ (· | ·) is a primitive notion that applies over conditional events of the form “ ϕgiven ψ ”, where ψ is not the impossible event. Our approach exploits an idea already used by Hájek and colleagues to define a logic for (unconditional) probability in the frame of fuzzy logics. Namely, in our logic for each pair of classical propositions ϕ and ψ, we take the probability of the conditional event “ ϕgiven ψ ”, ϕ ∣ ψ for short, as the truth-value of the (fuzzy) modal proposition P ( ϕ | ψ ), read as “ ϕ ∣ ψ is probable”. Based on this idea we define a fuzzy modal logic FCP(ŁΠ), built up over the many-valued logic Ł \(\Pi\frac{1}{2}\) (a logic which combines the well-known Lukasiewicz and Product fuzzy logics), which is shown to be complete with respect to the class of probabilistic Kripke structures induced by coherent conditional probabilities. Finally, we show that checking coherence of a probability assessment to an arbitrary family of conditional events is tantamount to checking consistency of a suitable defined theory over the logic FCP(ŁΠ).

UAI Conference 2004 Conference Paper

A Logic Programming Framework for Possibilistic Argumentation with Vague Knowledge

• Carlos Iván Chesñevar
• Guillermo Ricardo Simari
• Teresa Alsinet
• Lluís Godo

Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible argumentation formalism based on an extension of logic programming. Although DeLP has been successfully integrated in a number of different real-world applications, DeLP cannot deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper introduces P-DeLP, a new logic programming language that extends original DeLP capabilities for qualitative reasoning by incorporating the treatment of possibilistic uncertainty and fuzzy knowledge. Such features will be formalized on the basis of PGL, a possibilistic logic based on Godel fuzzy logic.

UAI Conference 2000 Conference Paper

A Complete Calcultis for Possibilistic Logic Programming with Fuzzy Propositional Variables

• Teresa Alsinet
• Lluís Godo

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy propositional variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy propositional variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.

UAI Conference 1999 Conference Paper

On the Semantics and Automated Deduction for PLFC, a Logic of Possibilistic Uncertainty and Fuzziness

• Teresa Alsinet
• Lluís Godo
• Sandra A. Sandri

Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a proof procedure based on a refutation complete resolution-style calculus. Recently, a syntactical extension of first order Possibilistic logic (called PLFC) dealing with fuzzy constants and fuzzily restricted quantifiers has been proposed. Our aim is to present steps towards both the formalization of PLFC itself and an automated deduction system for it by (i) providing a formal semantics; (ii) defining a sound resolution-style calculus by refutation; and (iii) describing a first-order proof procedure for PLFC clauses based on (ii) and on a novel notion of most general substitution of two literals in a resolution step. In contrast to standard Possibilistic logic semantics, truth-evaluation of formulas with fuzzy constants are many-valued instead of boolean, and consequently an extended notion of possibilistic uncertainty is also needed.

ECAI Conference 1998 Conference Paper

Possibilistic-Based Bidding Strategies in Electronic Auctions

• Pere Garcia
• Eduardo Giménez 0002
• Lluís Godo
• Juan A. Rodríguez-Aguilar

UAI Conference 1995 Conference Paper

Fuzzy logic and probability

• Petr Hájek 0001
• Lluís Godo
• Francesc Esteva

In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, here we propose a {em fuzzy} logic of probability for which completeness results (in a probabilistic sense) are provided. The main idea behind this approach is that probability values of crisp propositions can be understood as truth-values of some suitable fuzzy propositions associated to the crisp ones. Moreover, suggestions and examples of how to extend the formalism to cope with conditional probabilities and with other uncertainty formalisms are also provided.

UAI Conference 1994 Conference Paper

On Modal Logics for Qualitative Possibility in a Fuzzy Setting

• Petr Hájek 0001
• Dagmar Harmancová
• Francesc Esteva
• Pere Garcia
• Lluís Godo

Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative modal logic to the many--valued analogues MVS5 and MVKD45 of the well known modal logics of knowledge and belief S5 and KD45 respectively. Completeness results are obtained for such logics and therefore, they extend previous existing results for qualitative possibilistic logics in the classical non-fuzzy setting.

ECAI Conference 1992 Conference Paper

A Specialisation Calculus to Improve Expert Systems Communication

• Josep Puyol-Gruart
• Lluís Godo
• Carles Sierra

UAI Conference 1992 Conference Paper

A Symbolic Approach to Reasoning with Linguistic Quantifiers

• Didier Dubois
• Henri Prade
• Lluís Godo
• Ramón López de Mántaras

This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogism, modelling the chaining of probabilistic rules, is studied in this context. It is shown that a qualitative counterpart of this syllogism makes sense, and is relatively independent of the threshold defining the linguistically meaningful intervals, provided that these threshold values remain in accordance with the intuition. The inference power is less than that of a full-fledged probabilistic con-quaint propagation device but better corresponds to what could be thought of as commonsense probabilistic reasoning.

UAI Conference 1991 Conference Paper

Combining Multiple-valued Logics in Modular Expert Systems

• Jaume Agustí-Cullell
• Francesc Esteva
• Pere Garcia
• Lluís Godo
• Carles Sierra