On compositional reasoning about anonymity and privacy in epistemic logic

We introduce KBE, a modal epistemic logic for reasoning about Knowledge, Belief and Estimation, three attitudes involved in an agent's decision-making process. In our logic, Knowledge and Belief are captured by S4.2, a modal logic holding a distinguished position among the epistemic logics investigated in AI and Philosophy. The Estimation operator of KBE is a kind of generalized 'many' or 'most' quantifier, whose origins go back to the work of J. Burgess and A. Herzig, but its model-theoretic incarnation ('weak filters') has been introduced by K. Schlechta and V. Jauregui. We work with complete weak filters ('weak ultrafilters') as we are interested in situations where an estimation can be always reached. The axiomatization of KBE comprises 'bridge' axioms which reflect the intuitive relationship of 'estimation' to 'knowledge' and 'belief', several introspective properties are shown to hold and it comes out that believing i¾? can be equivalently defined in KBE as 'estimating that i¾? is known', an interesting fact and an indication of the intuitive correctness of the introduced estimation operator. The model theory of KBE comprises a class of frames combining relational Kripke frames with Scott-Montague semantics, in which neighborhoods are collections of 'large' sets of possible worlds. Soundness and completeness is mentioned and a tableaux proof procedure is sketched.

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

Epistemic Logic and Information Update

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.

With the amount of information available to us today, making sense of potentially conflicting information is a problem that we are bound to run into. We aim to study this problem from the perspective of epistemic logic. So far, we have studied logics for reasoning about information distributed across groups of agents in the epistemic logic framework, focusing on the notion of distributed belief. We have introduced the notions of cautious and bold distributed belief. These are intended as alternatives to the standard distributed belief, behaving better when agents have conflicting beliefs. With standard distributed belief, such situations lead to explosion: everything becomes distributedly believed. The idea behind the new notions is that we look at maximal consistent subgroups, allowing us to meaningfully express that a group collectively possesses information supporting a belief, also in cases where some group members disagree. Going forward, we are interested in continuing to explore the aggregation of potentially conflicting information in the setting of epistemic logic, e.g. by looking at distributed belief in richer extensions of epistemic logic and in relation to other areas that deal with similar problems.

The paper provides, for the first time, an analysis of the connected components (CC) grouping process, capable of predicting the grouping quality in terms of measurable, meaningful quantities. The results may also be used for design, and specifically for choosing the parameters controlling the grouping process. Unlike most previous statistical methods in computer vision, which were based on an independence assumption, we confront the predictions with the actual results and show that a model, which takes into account statistical dependence, may predict performance better. This paper is concerned with simple grouping processes based on the connected components graph algorithm. Such processes are very fast and are linear in the number of data features. The performance of the algorithm is considered under a probabilistic setting where both the image and the grouping cues are random variables, it focuses on analyzing the quality of the groups extracted by this algorithm, and shows that quantitative and meaningful measures of grouping quality may be predicted and even, within certain constraints, controlled. In particular, we consider two measures of grouping quality: the number of background features, which are falsely added to the true groups and the number of parts to which a smooth curve (i.e. true group) is fragmented.

A description is given of an empirical study of the failure characteristics of software defects detected in the programs developed in the Project on Diverse Software (PODS). The results are interpreted in the context of a state machine model of software failure. The results of the empirical study case doubts on the general validity of the assumption of constant software failure probability and the assumption of constant software failure probability and the assumption that all defects have similar failure rates. In addition, an analysis of failure dependency lends support to the use of diversity as a means of minimizing the impact of design-level faults. Here, nonidentical faults exhibited coincident failure characteristics approximately in accord with the independence assumption, and some of the observed positive and negative correlation effects could be explained by failure masking effects, which can be removed by suitable design. >

Model checking as an approach to the automatic verification of finite state systems has focussed predominantly on system specifications expressed in temporal logic. In the distributed systems community, logics of knowledge (epistemic logics) have been advocated for expressing desirable properties of protocols and systems. A range of logics combining temporal and epistemic components have been developed for this purpose. However, the model checking problem for temporal logics of knowledge has received (comparatively) little attention. In this paper, we address ourselves to this problem. Following a brief survey of the relevant issues and literature, we introduce a temporal logic of knowledge (Halpern and Vardi’s logic CKL n). We then develop an approach to CKL n model checking that combines ideas from the interpreted systems semantics for knowledge with the logic of local propositions developed by Engelhardt et al. With our approach, local propositions provide a means to reduce CKL n model checking to linear temporal logic model checking. After introducing and exploring the ideas underpinning our approach, we present a case study (the bit transmission problem) in which spin was used to establish temporal epistemic properties of a system implemented in PROMELA.

We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently introduced logic first-order theory of random variables with probabilistic independence. We give several results that compare the expressivity of these logics with the most studied logics in probabilistic team semantics setting, as well as relating their expressivity to a numerical variant of second-order logic. In addition, we introduce novel entropy atoms and show that the extension of first-order logic by entropy atoms subsumes probabilistic independence logic. Finally, we obtain some results on the complexity of model checking, validity and satisfiability of our logics.

A breaking index appeared in the Boussinesq-type numerical model (Lynett, 2006) is replaced and tested. The new breaking index, which includes the water depth effect and is not sensitive to the spatial grid length, was first proposed by the Smith and Kraus (1991) and further optimized by many experimental data in this study. The numerical tests show that the modified Lynett's model with this new breaking index is more stable and efficient in the nearshore breaking point computations. Comparison with Dingemans (1994) experiment shows the validity of the modified Lynett's model in the nearshore wave breaking simulation.

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.

A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations