M. Fitting and R. L. Mendelsohn. First-Order Modal Logic. Kluwer Academic Publishers, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with the flow of time #, it thus su#ces to associate with each n N a first order (i.e. a QL ) model n , P 0 , #. However, a more natural (and more powerful) semantics is obtained by additionally posing restrictions on the domains of these first order models; see e.g. [4, 6]. In what follows, we consider two kinds of temporal models: those with expanding domains, in which # n #m if n m, and those with constant domains, in which all domains # n are the same. Definition 2.2 (model) A is a triple M = I#, where # is the set of natural numbers equipped ....

M. Fitting and R. Mendelson. First-Order Modal Logic. Kluwer Academic Publishers, Dordrecht, 1998.

....constant, expanding, or contracting domains are assumed. As an immediate corollary, Beth s de nability theorem also holds for all such logics. 1 Quanti ed modal logic We quickly review the relevant model theory for quanti ed modal logic (QML) For a thorough treatment the reader is referred to [7]. The language of QML is obtained from the language of classical rst order predicate logic with identity by adding a unary operator 3. We only consider signatures without function symbols, but allow constants denoting individuals and nullary predicate symbols (that is, propositional symbols) We ....

M. Fitting and R. Mendelsohn. First{Order Modal Logic. Kluwer Academic Publishers, 1998.

....formulae over an abstracted K FO 3 structure are conservative. The semantics of 3 valued propositional modal logics is described in [3] Combining 3 valued modal logic with a first order language yields a 3 valued first order modal logic as the one used in this paper. The reader is referred to [23] for more details on first order modal logic. Given M FO 3 = #Sm , Rm , S 0 m , I m # and Q FO 3 = #S q , R q , S 0 q , I q #, two K FO 3 structures, a relation H # Sm S q is a simulation relation i# for every s m # Sm and s q # S q such that (s m , s q ) # H the ....

M. Fitting and R.L. Mendelsohn. First-Order Modal Logic, volume 277 of Synthese Library. Kluwer Academic Publishers, Dordrecht, 1998.

....propositional modal logic but some especially those involving knowledge representation need the extra expressivity offered by predicate modal logic. The standard introductory reference for propositional modal logic is [12] A very good recent text is [5] For first order modal logics [6] and [10] are good references. 73 The calculus is a logic of operators on modal sentences which includes the least fixed point and the greatest fixed point operators. Any modal language can be augmented with axioms for the calculus to allow construction of more complex operators from the ....

Melvin Fitting and Richard Mendelsohn. First-order Modal Logic. Kluwer Academic Publishers, 1999.

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M. Fitting and R.L. Mendelsohn. First-Order Modal Logic. Kluwer Academic Publishers, Dordrecht, 1998.

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M. Fitting and R.L. Mendelsohn. First-order Modal Logic. Kluwer Academic Publishers, 1998.

....the counterpart relations in some appropriate sense. Variables on the other hand simply denote objects in the domain of a given world. In the case of traditional semantics this asymmetry appears in a similar fashion if one allows constant symbols to be non rigid, as has been done e.g. in [5]. Then, variables denote transcendental entities, whereas constants denote something like individual concepts, i.e functions from possible worlds to a domain. Facing this dilemma, one solution to this is to completely move to a higher order setting, where constants and variables can be of various ....

....here is a shift from a de re to a de dicto interpretation. If we follow the traces of the objects, the formula is valid, but if we substitute intensional objects, namely constants, it becomes refutable. Notice that this situation is also re ected in the way, non rigid constants are treated in [5]. There, the two possible readings of the above formula, the de dicto and de re reading, are distinguished by actually binding the interpretation of the constants to the respective worlds by using the term binding operator. Applied to Hesperus and Phosphorus, this means that if they are equal, ....

Melvin Fitting and Richard L. Mendelsohn, First{Order Modal Logic, Kluwer Academic Publishers, Dordrecht, 1998.

....expanding, or contracting domains are assumed. As an immediate corollary, Beth s de nability theorem also holds for all such logics. 1 Quanti ed modal logic We quickly review the relevant model theory for quanti ed modal logic (QML) For a thorough treatment the reader is referred to [7]. The language of QML is obtained from the language of classical rst order predicate logic with identity by adding a unary operator 3. We only consider signatures without function 2 symbols, but allow constants denoting individuals and nullary predicate symbols (that is, propositional symbols) ....

M. Fitting and R. Mendelsohn. First{Order Modal Logic. Kluwer Academic Publishers, 1998.

....particular, proving liveness properties of such programs, e.g. that a thread is eventually created in response to each request made to a web server, can be a quite difficult task. The contributions of this paper can be summarized as follows: 1. We introduce a first order modal (temporal) logic [9, 8] that allows specifications of temporal properties of programs with dynamically evolving heaps to be stated in a natural manner. 2. We develop an abstract interpretation [4] for verifying that a program satisfies such a specification. 3. We implemented a prototype of the analysis using the TVLA ....

....contents to be maintained while abstracting away any information about the actual physical locations in the store. This gives rise to traces in which worlds along the trace may have different domains. Such traces can be seen as models of a first order modal logic with a varying domain semantics [8]. This could be equivalently, but less naturally, modelled using constantdomain semantics. This framework generalizes other specification methods that address dynamic allocation and deallocation of objects and threads. In particular, its descriptive power goes beyond Propositional LTL and ....

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M. Fitting and R.L. Mendelsohn. First-Order Modal Logic, volume 277 of Synthese Library. Kluwer Academic Publishers, Dordrecht, 1998.

....programs, e.g. that a thread is eventually created in response to a request made to a web server, can be a quite difficult task. 1.1 Main Results and Comparison to Previous Work The contributions of this paper can be summarized as follows: 1. We introduce a first order modal (temporal) logic [10, 9], that allows to give natural specifications of temporal properties of programs with dynamically evolving heaps. 2. We develop an abstract interpretation [4] for verifying that a program satis fies such a specification. 3. We implemented a prototype of the analysis using the TVLA system [12] ....

....of the the heap contents to be maintained while abstracting from the actual physical store location. This gives rise to traces in which configurations along the trace may have different universes. Such traces can be seen as models of a first order modal logic with a varying domain semantics [9]. This framework generalizes other specification methods that address dynamic allocation and deallocation of objects and threads. In particular, its descriptive power goes beyond PLTL and finite state machines (e.g. 2] 3] introduces the Bandera Specification Language (BSL) which allows the ....

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M. Fitting and R. Mendelsohn. First-Order Modal Logic, volume 277 of Synthese Library. Kluwer Academic Publishers, Dordrecht, 1998.

....properties in a state where the individual does not exist. The assumption of constant domains corresponds to the validity of the Barcan formula #x#A # ##xA and the assumption of increasing domains corresponds to the validity of the converse Barcan formula ##xA # #x#A. We refer to the recent [15] for an overview of discussions of these and related matters. There is a whole web of mathematical questions related the Barcan formula and its variations. As to proof theoretical aspects, the standard ordinary sequent calculus for K uses Gentzen sequents # # # and comprises just one ....

M. Fitting and R.L. Mendelsohn. First-order Modal Logic. Kluwer Academic Publishers, 1998.

....see, hybridization allows us to repair failures of interpolation in rst order modal logic, in a very general way. This abstract is not self contained. For rst order modal logic (and in particular, a discussion of varying, expanding, contracting, and constant domains) see Fitting and Mendelsohn [4]. For Beth de nability and Craig iterpolation, see Chang and Keisler [2] As for hybrid logic, the most relevant points are the following. Hybrid logic contains special variables, written w, w 0 , which range over worlds. Pre xing a formula by #w binds the variable w to the world of ....

M. Fitting and R. Mendelsohn. First{Order Modal Logic. Kluwer Academic Publishers, 1998. 2

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M. Fitting and R. L. Mendelsohn. First-Order Modal Logic. Kluwer Academic Publishers, 1998.

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Melvin Fitting and Richard L. Mendelsohn. FirstOrder Modal Logic. Kluwer Academic Publishers, 1998.

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Fitting, M., Mendelsohn, R. L.: First-Order Modal Logic, Kluwer Academic Publishers, 1999.

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Fitting, M., Mendelsohn, R. L.: First-Order Modal Logic, Kluwer Academic Publishers, 1999.

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Melvin Fitting. Types, Tableaus, and Godel's God. Kluwer Academic Publishers, 2002.

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Fitting, M., Mendelsohn, R. L.: First-Order Modal Logic, Kluwer Academic Publishers, 1999.

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