Abstract Public announcement logic (PAL) extends multi-agent epistemic logic with dynamic operators modelling the effects of public communication. Allowing quantification over public announcements lets us reason about theexistenceof an announcement that reaches a certain epistemic goal. Two notable examples of logics of quantified announcements are arbitrary public announcement logic (APAL) and group announcement logic (GAL). While the notion of common knowledge plays an important role in PAL, and in particular in characterisations of epistemic states that an agent or a group of agents might make come about by performing public announcements, extensions of APAL and GAL with common knowledge still haven’t been studied in detail. That is what we do in this paper. In particular, we consider both conservative extensions, where the semantics of the quantifiers is not changed, as well as extensions where the scope of quantification also includes common knowledge formulas. We compare the expressivity of these extensions relative to each other and other connected logics, and provide sound and complete axiomatisations. Finally, we show how the completeness results can be used for other logics with quantification over information change.

Several different notions of group knowledge have been extensively studied in the epistemic and doxastic logic literature, including common knowledge, general knowledge (everybody-knows) and distributed knowledge. In this paper we study a natural notion of group knowledge between general and distributed knowledge: somebody-knows. While something is general knowledge if and only if it is known by everyone, this notion holds if and only if it is known by someone. This is stronger than distributed knowledge, which is the knowledge that follows from the total knowledge in the group. We introduce a modality for somebody-knows in the style of standard group knowledge modalities, and study its properties. Unlike the other mentioned group knowledge modalities, somebody-knows is not a normal modality; in particular it lacks the conjunctive closure property. We provide an equivalent neighbourhood semantics for the language with a single somebody-knows modality, together with a completeness result: the somebody-knows modalities are completely characterised by the modal logic EMN extended with a particular weak conjunctive closure axiom. We also show that the satisfiability problem for this logic is PSPACE-complete. The neighbourhood semantics and the completeness and complexity results also carry over to logics for so-called local reasoning (Fagin et al. 1995) with bounded ``frames of mind'', correcting an existing completeness result in the literature (Allen 2005).

Abstract While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group belief under different assumptions about the properties of belief. In particular, we map out (lack of) preservation of belief properties against different standard definitions of group belief. It turns out that what is called group belief most often is not actually belief, i.e. does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, neither common belief (does not satisfy the negative introspection axiom 5) nor distributed belief (does not satisfy the consistency axiom D) are not actually belief. There has been some confusion in the literature regarding soundness of proposed axiomatizations of logics with distributed knowledge, related to the mentioned lack of preservation. In this paper we also present detailed completeness proofs of sound and complete axiomatizations of KD45 with distributed belief, both with and without common belief.

Abstract In this paper, we show that modal logics for reasoning about social choice quickly become undecidable. In particular, we study modal logics that can be used to reason about situations involving both actual and claimed preferences in the context of a social choice function and argue that reasoning on this level often occurs in social choice. We formally define a particular logic, interpreted in such situations, that can express the properties involved in the Gibbard–Satterthwaite theorem. We then, however, demonstrate that any modal logic interpreted in such situations having a certain natural expressive power, in particular a modality quantifying over all possible claimed preferences, becomes undecidable when there are enough agents in the system. We also discuss a decidable special case and provide a complete axiomatization of fragment of the language.

Abstract This paper proposes different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization based on balance theory. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this work, we examine different possibilities for extending this basic language to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms. Furthermore, we define the property of full balance rather than balanced-up-to-a-degree. We look into the complexity of the model checking problem and show a non-compactness result of the extended language. Along the way, we provide axioms for weak balance. We also look at a full hybrid extension and reason about network changes with dynamic modalities. Then, to explore the measures of how far a network is from polarization, we consider variations of measures in relation to balance.

Abstract Coalition logic is currently one of the most popular logics for multi-agent systems. While logics combining coalitional and epistemic operators have received considerable attention, completeness results for epistemic extensions of coalition logic have so far been missing. In this paper we provide several such results and proofs. We prove completeness for epistemic coalition logic with common knowledge, with distributed knowledge, and with both common and distributed knowledge, respectively. Furthermore, we completely characterise the complexity of the satisfiability problem for each of the three logics. We also study logics with interaction axioms connecting coalitional ability and knowledge.

This special issue of the Journal of Logic and Computation contains a selection of papers presented at the 11th Conference on Logic and the Foundations of the Theory of Games and Decisions (LOFT11), which took place in Bergen (Norway), July 27–30, 2014. 1 LOFT11 marked 20 years of LOFT conferences: the first conference took place in 1994 in Marseille (France) and, since then, LOFT has become a regular bi-annual event. 2 The LOFT conferences are interdisciplinary events that bring together researchers from a variety of fields: cognitive psychology, computer science and artificial intelligence, economics, game theory, linguistics, logic, mind sciences, philosophy and social choice. In its original conception, LOFT had as its central theme the application of logic, in particular modal epistemic logic, to foundational issues in the theory of games and individual decision-making. Epistemic considerations have been central to game theory for a long time. The expression ‘interactive epistemology’ has been used in the game-theory literature to refer to the analysis of strategic interaction based on an explicit modelling of the players' beliefs about each other's beliefs and rationality. The LOFT conferences arose from the realization that the tools and methodology that were used in game theory were closely related to those used in other fields, notably computer science, logic and philosophy. Modal logic turned out to be the common language that made it possible to bring together different professional communities.

João Leite, Paolo Torroni, Thomas Ågotnes, Guido Boella, Leendert van der Torre; Preface to the Special Issue on Computational Logic in Multi-Agent Systems (CLI

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as "Ann knows that Bill is aware of something Ann is not aware of" - without using a stronger statement such as "Ann knows that Bill is aware of p and Ann is not aware of p", for some particular p. Recently, however, Halpern and Rêgo (2006) introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. The logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of The logic is less expressive than Halpern's and Rêgo's logic. It is, however, expressive enough to express all of Halpern's and Rêgo's motivating examples. In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete.

In Alternating-time Temporal Logic (ATL), one can express statements about the strategic ability of an agent (or a coalition of agents) to achieve a goal ϕ such as: "agent i can choose a strategy such that, if i follows this strategy then, no matter what other agents do, ϕ will always be true". However, strategies in ATL are revocable in the sense that in the evaluation of the goal ϕ the agent i is no longer restricted by the strategy she has chosen in order to reach the state where the goal is evaluated. In this paper we consider alternative variants of ATL where strategies, on the contrary, are irrevocable. The difference between revocable and irrevocable strategies shows up when we consider the ability to achieve a goal which, again, involves (nested) strategic ability. Furthermore, unlike in the standard semantics of ATL, memory plays an essential role in the semantics based on irrevocable strategies.

The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: ‘knowing at least’ a set of formulae and ‘knowing at most’ a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise non-omniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics, such as Ågotnes and Walicki (2004, Proc. 2nd EUMAS, pp. 1–10), Alechina et al. (2004, Proc. 3rd AAMAS, pp. 601–613), Duc (1997, J. Logic Comput., 7, 633–648).