In systems such as group calendars or collaborative platforms, agents make group commitments to future actions that must adapt as new facts or constraints emerge. We develop a formal framework for revising such group intentions in systems where coalitions adopt shared, temporally extended intentions represented in a logic based on Alternating-Time Temporal Logic with strategy contexts. After formulating coherence criteria for systems of group intentions, we establish representation theorems in the style of Katsuno and Mendelzon, showing that revision operators satisfy rationality postulates precisely when they can be represented by preorders on strategy profiles. These results extend classical revision theory by covering non-total preorders and a logic of higher expressive power. Altogether, the framework lays the groundwork for principled revision of group intentions in systems where both coordination and change are essential.

This paper investigates complex argumentation settings, called weighted higher-order argumentation frameworks (wHO-AFs), where both arguments and attacks carry initial weights and may be subject to attacks from arguments. It focuses on developing gradual semantics capable of rationally evaluating these elements by assigning each argument and attack a numerical value, representing their respective degrees of acceptance and seriousness. The contributions of the paper are five-fold: i) It identifies key technical challenges for semantics in wHO-AFs, such as handling the distinction between arguments and attacks, and determining how their values should be combined. To address these challenges, the paper introduces a set of guiding principles that capture various semantic strategies. ii) It introduces a broad family of semantics that treat arguments and attacks uniformly, evaluating them in the same way. This family encompasses both semantics inspired by extension-based approaches and those that are purely gradual. iii) It defines a second extensive family of semantics that differentiate between arguments and attacks. This includes instances where a single function evaluates both types of elements, as well as hybrid variants that apply distinct evaluation functions to arguments and attacks. iv) It offers a formal analysis and comprehensive comparison of the resulting diverse semantics. v) It presents an empirical evaluation of these semantics. The results are promising as they show that the values of all elements can be computed in fewer than 20 iterations, even for large frameworks, while maintaining very low runtime. The paper ultimately delivers a catalogue of semantics, each offering distinct formal properties and behaviors, contributing a flexible toolkit for reasoning in rich argumentative contexts.

Structural equation models (SEM) are a standard approach to representing causal dependencies between variables. In this paper we propose a new interpretation of existing formalisms in the field of Actual Causality in which SEM's are viewed as mechanisms transforming the dynamics of exogenous variables into the dynamics of endogenous variables. This allows us to combine counterfactual causal reasoning with existing temporal logic formalizms, and to introduce a temporal logic, CPLTL, for causal reasoning about such structures. Then, we demonstrate that the standard restriction to so-called recursive models (with no cycles in the dependency graphs) is not necessary in our approach. This fact provides us extra tools for reasoning about mutually dependent processes and feedback loops. Finally, we introduce the notions of model equivalence for temporal causal models and show that CPLTL has an efficient model-checking procedure.

Tracing and analysing the responsibility for unsafe outcomes of actors' decisions in multi-agent settings have been studied in recent years. These studies often focus on deterministic scenarios and assume that the unsafe outcomes for which actors can be held responsible are actually realized. This paper considers a broader notion of responsibility where unsafe outcomes are not necessarily realized, but their probabilities are unacceptably high. We present a logic combining strategic, probabilistic and temporal primitives designed to express concepts such as the risk of an undesirable outcome and being responsible for exceeding a risk threshold in one-shot games. We demonstrate that the proposed logic is (weakly) complete, decidable and has an efficient model-checking procedure. Finally, we define a probabilistic notion of responsibility and study its formal properties in the proposed logic setting.

This work presents a proof-theoretical and model-theoretical approach to probabilistic temporal logic . We present two novel logics; each of them extends both the language of linear time logic (LTL) and the language of probabilistic logic with polynomial weight formulas. The first logic is designed for reasoning about probabilities of temporal events, allowing statements like “the probability that A will hold in next moment is at least the probability that B will always hold” and conditional probability statements like “probability that A will always hold, given that B holds, is at least one half”, where A and B are arbitrary statements. We axiomatize this logic, provide corresponding sigma additive semantics and prove that the axiomatization is sound and strongly complete. We show that the satisfiability problem for our logic is decidable, by presenting a procedure which runs in polynomial space. We also present a logic with much richer language, in which probabilities are not attached only to temporal events, but the language allows arbitrary nesting of probability and temporal operators, allowing statements like “probability that tomorrow the chance of rain will be less than 80% is at least a half”. For this logic we prove a decidability result.

There have been a number of attempts to develop a formal definition of causality that accords with our intuitions about what constitutes a cause. Perhaps the best known is the “modified” definition of actual causality, HPm, due to Halpern. In this paper, we argue that HPm gives counterintuitive results for some simple causal models. We propose Dynamic Causality (DC), an alternative semantics for causal models that leads to an alternative definition of causes. DC ascribes the same causes as HPm on the examples of causal models widely discussed in the literature and ascribes intuitive causes for the kinds of causal models we consider. Moreover, we show that the complexity of determining a cause under the DC definition is lower than for the HPm definition.

Gradual semantics are methods that evaluate overall strengths of individual arguments in graphs. In this paper, we investigate gradual semantics for extended frameworks in which probabilities are used to quantify the uncertainty about arguments and attacks belonging to the graph. We define the likelihoods of an argument’s possible strengths when facing uncertainty about the topology of the argumentation framework. We also define an approach to compare the strengths of arguments in this probabilistic setting. Finally, we propose a method to calculate the overall strength of each argument in the framework, and we evaluate this method against a set of principles.

Compensation is a strategy that a semantics may follow when it faces dilemmas between quality and quantity of attackers. It allows several weak attacks to compensate one strong attack. It is based on compensation degree, which is a tuple that indicates (i) to what extent an attack is weak and (ii) the number of weak attacks needed to compensate a strong one. Existing principles on compensation do not specify the parameters, thus it is unclear whether semantics satisfying them compensate at only one degree or several degrees, and which ones. This paper proposes a parameterised family of gradual semantics, which unifies multiple semantics that share some principles but differ in their strategy regarding solving dilemmas. Indeed, we show that the two semantics taking the extreme values of the parameter favour respectively quantity and quality, while all the remaining ones compensate at some degree. We define three classes of compensation degrees and show that the novel family is able to compensate at all of them while none of the existing gradual semantics does.

To build a theory of intention revision for agents operating in stochastic environments, we need a logic in which we can explicitly reason about their decision-making policies and those policies' uncertain outcomes. Towards this end, we propose PLBP, a novel probabilistic temporal logic for Markov Decision Processes that allows us to reason about policies of bounded size. The logic is designed so that its expressive power is sufficient for the intended applications, whilst at the same time possessing strong computational properties. We prove that the satisfiability problem for our logic is decidable, and that its model checking problem is PSPACE-complete. This allows us to e.g. algorithmically verify whether an agent's intentions are coherent, or whether a specific policy satisfies safety and/or liveness properties.

The need for tools and techniques to formally analyze and trace the responsibility for unsafe outcomes to decision-making actors is urgent. Existing formal approaches assume that the unsafe outcomes for which actors can be held responsible are actually realized. This paper considers a broader notion of responsibility where unsafe outcomes are not necessarily realized, but their probabilities are unacceptably high. We present a logic combining strategic, probabilistic and temporal primitives designed to express concepts such as the risk of an undesirable outcome and being responsible for exceeding a risk threshold. We demonstrate that the proposed logic is complete and decidable.

We present a proof-theoretical and model-theoretical approach to reasoning about knowledge and conditional probability. We extend both the language of epistemic logic and the language of linear weight formulas, allowing statements like “Agent Ag knows that the probability of A given B is at least a half”. We present both a propositional and a first-order version of the logic. We provide sound and complete axiomatizations for both logics and we prove decidability in the propositional case.

An argumentation framework is a pair made of a graph and a semantics. The nodes and the edges of the graph represent respectively arguments and relations (e.g., attacks, supports) between arguments while the semantics evaluates the strength of each argument of the graph. This paper investigates gradual semantics dealing with weighted graphs, a family of graphs where each argument has an initial weight and may be attacked by other arguments. It contains four contributions. The first consists of laying the foundations of gradual semantics by proposing key principles on which evaluation of argument strength may be based. Foundations are important not only for a better understanding of the evaluation process in general, but also for clarifying the basic assumptions underlying semantics, for comparing different (families of) semantics, and for identifying families of semantics that have not been explored yet. The second contribution consists of providing a formal analysis and a comprehensive comparison of the semantics that have been defined in the literature for evaluating arguments in weighted graphs. As a third contribution, the paper proposes three novel semantics and shows which principles they satisfy. The last contribution is the implementation and empirical evaluation of the three novel semantics. We show that the three semantics are very efficient in that they compute the strengths of arguments in less than 20 iterations and in a very short time. This holds even for very large graphs, meaning that the three semantics scale very well.

Abstract In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.

Bipolar argumentation studies argumentation graphs where attacks are combined with another relation between arguments. Many kind of relations (e.g. deductive support, evidential support, necessities etc.) have been defined and investigated from a Dung semantics perspective. We place ourselves in the context of argumentation systems with necessities and provide the first study to investigate ranking semantics in this setting. To this end, we (1) provide a set of postulates specifically designed for necessities and (2) propose the first ranking-based semantics in the literature to be shown to respect these postulates.

We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. We define its syntax and semantics and prove the strong completeness property of the corresponding axiomatic system. 1

Several argument-based logics have been defined for handling inconsistency in propositional knowledge bases. We show that they may miss intuitive consequences, and discuss two sources of this drawback: the definition of logical argument i) may prevent formulas from being justified, and ii) may allow irrelevant information in argument's support. We circumvent these two issues by considering a general definition of argument and compiling each argument. A compilation amounts to forgetting in an argument's support any irrelevant variable. This operation returns zero, one or several concise arguments, which we then use in an instance of Dung's abstract framework. We show that the resulting logic satisfies existing rationality postulates, namely consistency and closure under deduction. Furthermore, it is more productive than the existing argument-based and coherence-based logics.

The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

We introduce a logic for temporal beliefs and intentions based on Shoham's database perspective and we formalize his coherence conditions on beliefs and intentions. In order to do this we separate strong beliefs from weak beliefs. Strong beliefs are independent from intentions, while weak beliefs are obtained by adding intentions to strong beliefs and everything that follows from that. We provide AGM-style postulates for the revision of strong beliefs and intentions: strong belief revision may trigger intention revision, but intention revision may only trigger revision of weak beliefs. After revision, the strong beliefs are coherent with the intentions. We show in a representation theorem that a revision operator satisfying our postulates can be represented by a pre-order on interpretations of the beliefs, together with a selection function for the intentions.

Spatiotemporal databases can be used to efficiently store and retrieve information about objects moving in space and time. Probabilities are added to model the case where the locations are not known with certainty. A few years ago a new formalism was introduced to represent such information in the form of atomic formulas, each of which represents the probability (in the form of an interval because even the probabilities are not known precisely) that a particular object is in a particular location at a particular time. We extend this formalism to obtain several different probabilistic logics by adding logical operators. Furthermore, we axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and complete, and discuss decidability issues. While we relate these logics to previous axiomatizations of probabilistic logics, this article is self-contained: no prior knowledge of probabilistic logics is assumed.