Logics for Information Aggregation

What do epistemic logic and cognitive science have to do with each other?

Epistemic Logic and Information Update

In this paper, we exploit epistemic logic (or the modal logic of knowledge) for multiagent systems to discuss the compositionality of several privacy-related information-hiding/disclosure properties. The properties considered here are anonymity, privacy, onymity, and identity. Our initial observation reveals that anonymity/privacy properties are not necessarily sequentially compositional. This means that even though a system comprising several sequential phases satisfies a certain unlinkability property in each phase, the entire system does not always enjoy a desired unlinkability property. We show that the compositionality can be guaranteed provided that the phases of the system satisfy what we call independence assumptions. More specifically, we develop a series of theoretical case studies of what assumptions are sufficient to guarantee the sequential compositionality of various degrees of anonymity, privacy, onymity, and/or identity properties. Similar results for parallel composition are also discussed. Further, we use the probabilistic extension of epistemic logic to consider the compositionality of probabilistic anonymity/privacy. We show that the compositionality can also be guaranteed in the probabilistic setting, provided that the phases of the system satisfy a probabilistic independence assumption.

This paper presents a logic of questions developed as an extension of (S5) epistemic logic. We discuss many features that are important for erotetic logic (formalization and semantics of questions, answerhood conditions, and inferential structures with questions). The aim is to introduce an erotetic system which corresponds well with epistemic terms and can form an appropriate background for dynamic approaches in epistemic logic.

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.

The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant and hence not present in LP. For example, the choice function '+' in LP, which is specified by the condition s:F∨t:F → (s+t):F, is not necessarily symmetric. In this paper, we introduce an extension of the Logic of Proofs, SLP, which incorporates natural properties of the standard proof predicate in Peano Arithmetic: t is a code of a derivation containing F, including the symmetry of Choice. We show that SLP produces Brouwer-Heyting-Kolmogorov proofs with a rich structure, which can be useful for applications in epistemic logic and other areas.

We show that dynamic epistemic logic (DEL) is a substructural logic and that it is an extension of the update logic introduced in the companion article [12]. We identify axioms and inference rules that completely characterize the DEL product update, and we provide a sequent calculus for DEL. Finally, we show that DEL with a finite number of atomic events is as expressive as epistemic logic. In parallel, we provide a sequent calculus for update logic which turns out to be a generalization of the non-associative Lambek calculus.

Utterances of the subject’s intentional states were analyzed in the second half of the 20th century by researchers of epistemic logic. This approach was unable to complete the solution of the problem of logical omniscience because the subject of utterances does not always know all the consequences of their knowledge in everyday life. Sometimes the subject is convinced that contradictory utterances are true. In this way, epistemic logic idealizes the position of the subject in the analysis of utterances and, moreover, fixes them in one state. Because of this, the subject cannot expand and supplement their knowledge, because they already know all the logical consequences of utterances at the same time. This issue can be solved remaining within the framework of epistemic logic. In this case we have to weaken the subject’s cognitive potential for that, and, moreover, we have to take into account the subjective nature of utterances. This approach is based on the analysis of the implicit knowledge of the subject. So, it is important to pay attention on the object of utterances because the perceiver’s attention is directed to it. In this regard, the author considers the analysis of utterances of intentional states of subject in situational semantics. Due to the latter, we take into account situations that the subject has in mind, and, moreover, we consider situations independently of the agent, based on the information provided by the context. It is semantics based on how the world, not the subject’s utterances about mental representations, such as knowledge, beliefs, etc., works. In this case, the information is part of the context; it exists independently of the subject and is extracted by them for further transformation into utterances. Also, situational semantics considers the object, which helps to learn more about the ontological aspect of this problem. This is due to the fact that the information that helps us analyze an utterance exists in situations, not in the subject’s attitudes. The author concludes that situational semantics appears to be a more universal method in the logical-semantic analysis of utterances of the subject’s intentional states, as compared to epistemic logic, because it allows us to consider various types of information of an utterance, not only that which corresponds to the propositional content.

Theory of Mind, the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a mental attribution modelling logical framework that is more in-line with findings in cognitive science. We introduce the setting and some of its technical features, and argue why it does justice to empirical observations, using it for modelling well-known False-Belief Tasks.

Multi-agent system (MAS) requires coordination mechanisms to facilitate dynamic collaboration of the intelligent components, with the goal of meeting local and global objectives. This paper deals with the issue of using dynamic epistemic default logic to offer a natural way of communication policies for the management of inter-agent exchanges in MAS. We first explore the communication protocols in MAS that operate in dynamic and highly uncertain environments, and then we add the constrained default sets to realize the extension of dynamic epistemic logic theory and restrict the agent’s inference behavior via constrained epistemic default reasoning. We also specify and reason the characteristic of the dynamic updating when agent meets incompatible knowledge in the logical framework that show the usefulness of logical tools carried out in the dynamic process of information acquisition.

Argument evaluation , one of the central problems in argumentation theory, consists in studying what makes an argument a good one. This paper proposes a formal approach to argument evaluation from the perspective of justification logic. We adopt a multi-agent setting, accepting the intuitive idea that arguments are always evaluated by someone. Two general restrictions are imposed on our analysis: non-deductive arguments are left out and the goal of argument evaluation is fixed: supporting a given proposition. Methodologically, our approach uses several existing tools borrowed from justification logic, awareness logic, doxastic logic and logics for belief dependence. We start by introducing a basic logic for argument evaluation, where a list of argumentative and doxastic notions can be expressed. Later on, we discuss how to capture the mentioned form of argument evaluation by defining a preference operator in the object language. The intuitive picture behind this definition is that, when assessing a couple of arguments, the agent puts them to a test consisting of several criteria (filters). As a result of this process, a preference relation among the evaluated arguments is established by the agent. After showing that this operator suffers a special form of logical omniscience, called preferential omniscience, we discuss how to define an explicit version of it, more suitable to deal with non-ideal agents. The present work exploits the formal notion of awareness in order to model several informal phenomena: awareness of sentences, availability of arguments and communication between agents and external sources (advisers). We discuss several extensions of the basic logic and offer completeness and decidability results for all of them.

Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from a logical perspective, we consider the elenchus as a dynamic exchange allowing Socrates’ respondents to revise their beliefs, on pain of inconsistency. By stressing this point, we represent this method as a process of belief revision in dynamic epistemic logic and provide a new logical solution to what Vlastos called the problem of the elenchus.

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: sφ expresses that φ is true after an arbitrary announcement ψ. As this includes the trivial announcement ⊤, one might as well say that sφ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation dφ expresses that there is an announcement after which φ. This gives a perspective on Fitch's knowability issues: for which formulas φ does it hold that φ → dKφ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.

The calculus of constructions as a framework for proof search with set variable instantiation

We contrast Bonanno's ‘Belief Revision in a Temporal Framework’ (Bonanno, 2008) with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of van Benthem et al. (2006b) with relational substitutions (van Benthem, 2004) for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences (Grove, 1988; Board, 2002; Baltag and Smets, 2006, 2008b), prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update (Baltag and Smets, 2008b) and preference substitution (van Benthem, 2004).