Online research in philosophy

Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore-sentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful’ as (...) ‘known after its announcement’ and ‘knowable’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition ϕ that is not known after its announcement but there is another announcement after which ϕ is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: ◊(Kϕ ∨ K¬ϕ). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable’ as ‘known after an announcement’. (shrink)

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is (...) nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents. (shrink)

Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely (...) connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties. (shrink)

Since it was first proposed by Moses, Shoham, and Tennenholtz, the social laws paradigm has proved to be one of the most compelling approaches to the offline coordination of multiagent systems. In this paper, we make four key contributions to the theory and practice of social laws in multiagent systems. First, we show that the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman provides an elegant and powerful framework within which to express and understand social laws for multiagent systems. (...) Second, we show that the effectiveness, feasibility, and synthesis problems for social laws may naturally be framed as atl model checking problems, and that as a consequence, existing atl model checkers may be applied to these problems. Third, we show that the complexity of the feasibility problem in our framework is no more complex in the general case than that of the corresponding problem in the Shoham–Tennenholtz framework (it is np-complete). Finally, we show how our basic framework can easily be extended to permit social laws in which constraints on the legality or otherwise of some action may be explicitly required. We illustrate the concepts and techniques developed by means of a running example. (shrink)

Understanding the flow of knowledge in multi-agent protocols is essential when proving the correctness or security of such protocols. Current logical approaches, often based on model checking, are well suited for modeling knowledge in systems where agents do not act strategically. Things become more complicated in strategic settings. In this paper we show that such situations can be understood as a special type of game – a knowledge condition game – in which a coalition “wins” if it is able to (...) bring about some epistemic condition. This paper summarizes some results relating to these games. Two proofs are presented for the computational complexity of deciding whether a coalition can win a knowledge condition game with and without opponents (Σ2P-complete and NP-complete respectively). We also consider a variant of knowledge condition games in which agents do not know which strategies are played, and prove that under this assumption, the presence of opponents does not affect the complexity. The decision problem without opponents is still NP-complete, but requires a different proof. (shrink)

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight (...) in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems. (shrink)

We extend our general approach to characterizing information to multi-agent systems. In particular, we provide a formal description of an agent''s knowledge containing exactly the information conveyed by some (honest) formula . Only knowing is important for dynamic agent systems in two ways. First of all, one wants to compare different states of knowledge of an agent and, secondly, for agent a''s decisions, it may be relevant that (he knows that) agent b does not know more than . There are (...) three ways to study the question whether a formula can be interpreted as minimal information. The first method is semantic and inspects minimal models for (with respect to some information order on states). The second one is syntactic and searches for stable expansions, minimal with respect to some language *. The third method is a deductive test, known as the disjunction property. We present a condition under which the three methods are equivalent. Then, we show how to construct the order by collecting layered orders. Focusing on the multi-agent case we identify languages * for various orders , and show how they yield different notions of honesty for different multi-modal systems. We then provide several tools for studying honesty types and illustrate their usefulness on a number of examples, for three modal systems of particular interest. Finally, we relate the different notions of minimal knowledge, and describe possible patterns of honesty for these systems. (shrink)

We demonstrate ways to incorporate nondeterminism in a system designed to formalize the reasoning of agents concerning their abilities and the results of the actions that they may perform. We distinguish between two kinds of nondeterministic choice operators: one that expresses an internal choice, in which the agent decides what action to take, and one that expresses an external choice, which cannot be influenced by the agent. The presence of abilities in our system is the reason why the usual approaches (...) towards nondeterminism cannot be used here. The semantics that we define for nondeterministic actions is based on the idea that composite actions are unravelled in the strings of atomic actions and tests that constitute them. The main notions used in defining this semantics are finite computation sequences and finite computation runs of actions. The results that we obtain meet our intuitions regarding events and abilities in the presence of nondeterminism. (shrink)

We present an epistemic default logic, based on the metaphore of a meta-level architecture. Upward reflection is formalized by a nonmonotonic entailment relation, based on the objective facts that are either known or unknown at the object level. Then, the meta (monotonic) reasoning process generates a number of default-beliefs of object-level formulas. We extend this framework by proposing a mechanism to reflect these defaults down. Such a reflection is seen as essentially having a temporal flavour: defaults derived at the meta-level (...) are projected as facts in a next object level state. In this way, we obtain temporal models for default reasoning in meta-level formalisms which can be conceived as labeled branching trees. Thus, descending the tree corresponds to shifts in time that model downward reflection, whereas the branching of the tree corresponds to ways of combining possible defaults. All together, this yields an operational or procedural semantics of reasoning by default, which admits one to reason about it by means of branching-time temporal logic. Finally, we define sceptical and credulous entailment relations based on these temporal models and we characterize Reiter extensions in our semantics. (shrink)

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)