Related papers: Product closure of some second-order modal logics
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…
The continuous modal mu-calculus is a fragment of the modal mu-calculus, where the application of fixpoint operators is restricted to formulas whose functional interpretation is Scott-continuous, rather than merely monotone. By…
Binary classifiers are traditionally studied by propositional logic (PL). PL can only represent them as white boxes, under the assumption that the underlying Boolean function is fully known. Binary classifiers used in practical applications…
In this survey we review dynamic epistemic logics with modalities for quantification over information change. Of such logics we present complete axiomatizations, focussing on axioms involving the interaction between knowledge and such…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
In this note, we show the class of finite, epistemic programs to be Turing complete. Epistemic programs is a widely used update mechanism used in epistemic logic, where it such are a special type of action models: One which does not contain…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
This article develops a novel framework for modal logic based on the idea of stratified actualization, rather than the classical model of global possible worlds. Traditional Kripke semantics treat modal operators as quantification over…
Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…
The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
We consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under answer set semantics. New information is incorporated into the current knowledge base subject to a causal rejection principle…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Arbitrary Arrow Update Logic is a dynamic modal logic that uses an arbitrary arrow update modality to quantify over all arrow updates. Some properties of this logic have already been established, but until now it remained an open question…
Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic epistemic logic with (i) an arrow update operator, which represents a particular type of information change and (ii) an arbitrary arrow update operator, which…
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…