Results 1  10
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156
Functional Translation and SecondOrder Frame Properties of Modal Logics
, 1995
"... Normal modal logics can be defined axiomatically as Hilbert systems, or semantically in terms of Kripke's possible worlds and accessibility relations. Unfortunately there are Hilbert axioms which do not have corresponding firstorder properties for the accessibility relation. For these logics ..."
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Cited by 26 (15 self)
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intuitively can be seen as functions mapping worlds to accessible worlds. In this paper we show that from a certain point of view this functional language is more expressive than the relational language, and that certain secondorder frame properties can be mapped to firstorder formulae expressed
Modal Deduction in SecondOrder Logic and Set Theory
 Journal of Logic and Computation
, 1997
"... We investigate modal deduction through translation into standard logic and set theory. Derivability in the minimal modal logic is captured precisely by translation into a weak, computationally attractive set theory \Omega\Gamma This approach is shown equivalent to working with standard firstorder t ..."
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Cited by 12 (7 self)
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translations of modal formulas in a theory of general frames. Next, deduction in a more powerful secondorder logic of general frames is shown equivalent with settheoretic derivability in an `admissible variant' of \Omega\Gamma Our methods are mainly modeltheoretic and settheoretic, and they admit
Semanticsbased translation methods for modal logics
 J. Log. Comput
, 1991
"... A general framework for translating logical formulae from one logic into another logic is presented. The framework is instantiated with two different approaches to translating modal logic formulae into predicate logic. The first one, the well known 'relational ' translation makes the moda ..."
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Cited by 45 (1 self)
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the modal logic's possible worlds structure explicit by introducing a distinguished predicate symbol to represent the accessibility relation. In the second approach, the 'functional ' translation method, paths in the possible worlds structure are represented by compositions of functions
Modal logic of time division
"... abstract. A logic LTD is defined, inspired by [37]. It is syntactically like basic modal logic with an additional unary operator but it has an intervalbased semantics on structures with arbitrary linear frames. □ψ is interpreted as meaning ‘the current interval has a finite partition whose all memb ..."
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Cited by 1 (1 self)
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members satisfy ψ. ’ LTD is translatable into weak monadic secondorder logic but not into firstorder logic. The expressive power and the decidability properties of LTD and its fragments are studied.
Optimised Modal Translation and Resolution
, 1997
"... This thesis studies the optimised functional translation of propositional modal logics to firstorder logic, and firstorder resolution as a means for realising modal reasoning. The optimised functional translation maps modal logics to a lattice of clausal logics, called path logics. The general app ..."
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Cited by 12 (2 self)
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This thesis studies the optimised functional translation of propositional modal logics to firstorder logic, and firstorder resolution as a means for realising modal reasoning. The optimised functional translation maps modal logics to a lattice of clausal logics, called path logics. The general
A Fixpoint Approach to SecondOrder Quantifier Elimination with Applications to Correspondence Theory
, 1995
"... This paper is about automated techniques for (modal logic) correspondence theory. The theory we deal with concerns the problem of finding fixpoint characterizations of modal axiom schemata. Given a modal schema and a semantics based method of translating modal formulae into classical ones, we try to ..."
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Cited by 32 (7 self)
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This paper is about automated techniques for (modal logic) correspondence theory. The theory we deal with concerns the problem of finding fixpoint characterizations of modal axiom schemata. Given a modal schema and a semantics based method of translating modal formulae into classical ones, we try
5 Model theory of modal logic
 Studies in Logic and Practical Reasoning. Vol
"... 1.2 Kripke frames and structures................................... 4 1.3 The standard translations into first and secondorder logic.................. 5 1.4 Theories and equivalence..................................... 6 1.5 Definability............................................. 7 ..."
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Cited by 1 (0 self)
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1.2 Kripke frames and structures................................... 4 1.3 The standard translations into first and secondorder logic.................. 5 1.4 Theories and equivalence..................................... 6 1.5 Definability............................................. 7
On the Correspondence Between Modal and Classical Logic: an Automated Approach
, 1993
"... The current paper is devoted to automated techniques in the correspondence theory. The theory we deal with concerns the problem of nding classical rstorder axioms corresponding to propositional modal schemas. Given a modal schema and a semantics based method of translating propositional modal formul ..."
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Cited by 26 (0 self)
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semantics, the technique we apply is much more general, as it is based on elimination of secondorder quantiers from formulas. We show many examples of application of the method. Those can also serve as new, automated proofs of considered correspondences. Keywords: automated theorem proving, correspondence
Loosely Guarded Fragment of FirstOrder Logic Has the Finite Model Property
, 2000
"... We show that the loosely guarded and packed fragments of firstorder logic have the finite model property. We use a construction of Herwig. We point out some consequences in temporal predicate logic and algebraic logic. AMS classification: Primary 03B20; Secondary 03B45, 03C07, 03C13, 03C30, 03G1 ..."
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Cited by 18 (3 self)
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15 Keywords: finite structures, modal logic, modal fragment, packed fragment 1 Introduction Perhaps because beginning students of modal logic are often told that modal logic is more expressive than firstorder logic and indeed has some secondorder expressive power, or perhaps because
Epistemic Quantified Boolean Logic: Expressiveness and Completeness Results
"... We introduce epistemic quantified boolean logic (EQBL), an extension of propositional epistemic logic with quantification over propositions. We show that EQBL can express relevant properties about agents ’ knowledge in multiagent contexts, such as “agent a knows as much as agent b”. We analyse the ..."
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the expressiveness of EQBL through a translation into monadic secondorder logic, and provide completeness results w.r.t. various classes of Kripke frames. Finally, we prove that model checking EQBL is PSPACEcomplete. Thus, the complexity of model checking EQBL is no harder than for (nonmodal) quantified boolean
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