The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.

A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...) Q°.B + BF is also proved. (shrink)

This article proposes an account of knowing-who constructions within a generalisation of Hintikka’s quantified epistemic logic employing the notion of a conceptual cover Aloni PhD thesis [1]. The proposed logical system captures the inherent context-sensitivity of knowing-wh constructions Boër and Lycan, as well as expresses non-trivial cases of so-called concealed questions Heim. Assuming that quantifying into epistemic contexts and knowing-who are linked in the way Hintikka had proposed, the context dependence of the latter will translate into a context dependence of (...) de re attitude ascriptions and this will result in a ready account of a number of traditionally problematic cases including Quine’s well-known double vision puzzles Quine. (shrink)

Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka [58]. Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of “knowing that”. However, knowledge is expressed in everyday life by using various other locutions such as “knowing whether”, “knowing what”, “knowing how” and so on (knowing-wh hereafter). Such knowledge expressions (...) are better captured in quantified epistemic logic, as was already discussed by Hintikka [58] and his sequel works at length. This paper aims to draw the attention back again to such a fascinating but largely neglected topic. We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe can balance expressivity and complexity, and capture the essential reasoning patterns about knowing-wh. We survey our recent line of work on the epistemic logics of ‘knowing whether”, “knowing what” and “knowing how” to demonstrate the use of this new approach. (shrink)

One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantifiers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantifiers are not present, this is not really a first-order logic, but it is not exactly propositional either. For propositional logics such as K, T and D, adding such machinery produces (...) a decidable logic, but adding it to S5 produces an undecidable one. Further, if an equality symbol is in the language, and interpreted by the equality relation, logics from K4 to S5 yield undecidable versions. (Thus transitivity is the villain here.) The proof of undecidability consists in showing that classical first-order logic can be embedded. (shrink)

We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...) the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)

The first amounts, roughly, to "It is necessarily the case that any President of the U.S. is a citizen of the U.S." But the second says, "the person who in fact is the President of the U.S, has the property of necessarily being a citizen of the U.S," Thus, while (2) is clearly true, it would be reasonable to consider (3) false.

We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment is decidable, and expressive enough to include interesting assertions.

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal (...) operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

abstract. A first-order dynamic epistemic logic is developed where the names of the agents are also terms in the sense of first-order logic. Consequently one can quantify over epistemic modalities. Us- ing constructs from dynamic logic one can express many interesting concepts. First-order update models are developed and added to the language as modalities.