Results 11  20
of
45
On the Minimum ManyValued Modal Logic over a Finite Residuated Lattice
, 2009
"... This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum mod ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones only evaluated in the idempotent elements and the ones evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truthconstants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truthconstants in the language.
A Complete FirstOrder Logic of Knowledge and Time
, 2008
"... We introduce and investigate quantified interpreted systems, a semantics to reason about knowledge and time in a firstorder setting. We provide an axiomatisation, which we show to be sound and complete. We utilise the formalism to study message passing systems (Lamport 1978; Fagin et al 1995) in a ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
We introduce and investigate quantified interpreted systems, a semantics to reason about knowledge and time in a firstorder setting. We provide an axiomatisation, which we show to be sound and complete. We utilise the formalism to study message passing systems (Lamport 1978; Fagin et al 1995) in a firstorder setting, and compare the results obtained to those available for the propositional case.
THE MODAL LOGIC OF FORCING
, 2007
"... Abstract. A set theoretical assertion ψ is forceable or possible, written ♦ ψ, if ψ holds in some forcing extension, and necessary, written � ψ, ifψ holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFCprovable principle ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. A set theoretical assertion ψ is forceable or possible, written ♦ ψ, if ψ holds in some forcing extension, and necessary, written � ψ, ifψ holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFCprovable principles of forcing are exactly those in the modal theory S4.2. 1.
Quantified Epistemic Logics with Flexible Terms
 LORI workshop on Logic, Rationality and Interaction, Beijing
, 2007
"... abstract. We present a family of quantified epistemic logics for reasoning about knowledge in multiagent systems. The language enjoys flexible terms with different denotations depending on the epistemic context in which they are interpreted. We present syntax and semantics of the language formally ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
abstract. We present a family of quantified epistemic logics for reasoning about knowledge in multiagent systems. The language enjoys flexible terms with different denotations depending on the epistemic context in which they are interpreted. We present syntax and semantics of the language formally and show completeness of an axiomatisation. We discuss the expressive features of the language by means of an example. 1
Common Knowledge and Quantification
"... The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the mon ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbertstyle axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable. 1 Introduction Ever since it became common knowledge that the intelligent behavior of an agent is based not only on her knowledge about the world but also on the knowledge about both her own and other agents' knowledge, logical formalisms desig...
Modal systems based on manyvalued logics
"... We propose a general semantic notion of modal manyvalued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We propose a general semantic notion of modal manyvalued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework.
Products Of `transitive' Modal Logics Without The (abstract) Finite Model Property
"... It is well known that many twodimensional products of modal logics with at least one `transitive' (but not `symmetric') component lack the product finite model property. Here we show that products of two `transitive' logics (such as, e.g., K4 K4, S4 S4, GrzGrz and GLGL) do not ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
It is well known that many twodimensional products of modal logics with at least one `transitive' (but not `symmetric') component lack the product finite model property. Here we show that products of two `transitive' logics (such as, e.g., K4 K4, S4 S4, GrzGrz and GLGL) do not have the (abstract) finite model property either. These are the first known examples of 2D modal product logics without the finite model property where both components are natural unimodal logics having the finite model property.
Nonfinitely axiomatisable twodimensional modal logics
, 2011
"... We show the first examples of recursively enumerable (even decidable) twodimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linea ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We show the first examples of recursively enumerable (even decidable) twodimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nestingdepth. 1
STRUCTURAL CONNECTIONS BETWEEN A FORCING CLASS AND ITS MODAL LOGIC
"... Every definable forcing class Γ gives rise to a corresponding forcing modality, for which □Γ ϕ means that ϕ is true in all Γ extensions, and the valid principles of Γ forcing are the modal assertions that are valid for this forcing interpretation. For example, [9] shows that if ZFC is consistent, t ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Every definable forcing class Γ gives rise to a corresponding forcing modality, for which □Γ ϕ means that ϕ is true in all Γ extensions, and the valid principles of Γ forcing are the modal assertions that are valid for this forcing interpretation. For example, [9] shows that if ZFC is consistent, then the ZFCprovably valid principles of the class of all forcing are precisely the assertions of the modal theory S4.2. In this article, we prove similarly that the provably valid principles of collapse forcing, Cohen forcing and other classes are in each case exactly S4.3; the provably valid principles of c.c.c. forcing, proper forcing, and others are each contained within S4.3 and do not contain S4.2; the provably valid principles of countably closed forcing, CHpreserving forcing and others are each exactly S4.2; and the provably valid principles of ω1preserving forcing are contained within S4.tBA. All these results arise from general structural connections we have identified between a forcing class and the modal logic of forcing to which it gives rise.
Representable Cylindric Algebras and ManyDimensional Modal Logics
, 2010
"... The equationally expressible properties of the cylindrifications and the diagonals in finitedimensional representable cylindric algebras can be divided into two groups: (i) ‘Onedimensional ’ properties describing individual cylindrifications. These can be fully characterised by finitely many equat ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
The equationally expressible properties of the cylindrifications and the diagonals in finitedimensional representable cylindric algebras can be divided into two groups: (i) ‘Onedimensional ’ properties describing individual cylindrifications. These can be fully characterised by finitely many equations saying that each ci, for i < n, is a normal (ci0 = 0), additive (ci(x+y) = cix+ciy) and complemented closure operator: x ≤ cix cicix ≤ cix ci(−cix) ≤ −cix. (1) (ii) ‘Dimensionconnecting ’ properties, that is, equations describing the diagonals and interaction between different cylindrifications and/or diagonals. These properties are much harder to describe completely, and there are many results in the literature on their complexity. The main aim of this chapter is to study generalisations of (i) while keeping (ii) as unchanged as possible. In other words, we would like to analyse how much of the complexity of RCAn is due to its ‘manydimensional ’ character and how much of it