Burgess J. [1984], Basic tense logic, in F. G. D. Gabbay, ed., `Handbook of Philosophical Logic', Reidel, chapter II. 2, pp. 89-134.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....family of contexts to which one can extend the eld of applicability of the set theoretic translation method, namely, modal logics extended with new modal operators. We will focus on the cases of the modal logic of inequality [17] the so called irre exivity rule [13] and minimal tense logic [10]. However, many other cases can be treated analogously and we will conclude the section with some comments on a general theory relative to such a technique. In [8] we have shown that there exists a straightforward solution to the problem of generalizing the set theoretic translation to any ....

....operator, and it also tells us that the comprehension we need to capture the notion of irre exivity is as much as we need for the basic machinery of the translation and strictly less of what we need for D. 4. 3 Minimal tense logic As another example, we consider the case of minimal tense logic TL [10]. TL extends propositional logic with two one place operators: F (future tense) and P (past tense) A sound and complete axiomatic system for TL consists of the usual axioms and rules of propositional logic plus the axioms: G(p q) Gp Gq) H(p q) Hp Hq) p GPp p HFp where G and H ....

J.P. Burgess, Basic Tense Logic, in Handbook of Philosophical Logic, Vol. II, D. Gabbay and F. Guenthner (eds.), D. Reidel Pub. Comp., Dordrecht-Holland, 1984, pp. 89-133.

.... in ordinary modal logic) Despite the unde nability of Antisymmetry, we can prove a completeness result for the class of antisymmetric two sorted frames: we will now show that MTL 0 is complete with respect to such frames; we use a technique based on Burgess chronicle construction (cf. Burgess [2]) De nition 2.3 Below we write ; for the canonical displacement relation 10 de ned in the proof of Theorem 2.1: if for all 2 , 2 . Let F = T; D; DIS) be a two sorted frame, and g an interpretation of the algebraic terms on F. A chronicle on F and g is a function such ....

....the spatial behavior of read and write heads of a hard disk. Developing this more liberal approach to interpreting metric temporal languages is part of our ongoing research. In this paper we have not discussed decidability issues. It is known that a negative result holds for Q MTL 0 . Burgess [2] shows that the decision problem for quanti ed metric temporal logic is equivalent to that for the set of all universal monadic second order formulae true in all ordered abelian groups, and he proves that the decision problem for the validity of rst order formulae involving a single binary ....

J.P. Burgess, Basic tense logic, in: D.M. Gabbay and F. Guenther, eds., Handbook of Philosophical Logic, Vol. 2 (Dordrecht, Reidel, 1984) 89-134.

.... to Prior s di erent grades of tense logical involvement [27] Research in philosophy, linguistics, and mathematical logic resulted in a family of (metric) tense logics that take time as a primitive notion and de ne (timed) states as sets of atomic propositions which are true at given times, e.g. [2, 6, 12, 14, 28]. In the last year, a few papers demonstrated the possibility of successfully exploiting metric (possibly layered) tense logics in computer science, e.g. 7, 15, 20, 21, 24] The present work further develops this research direction. Most research in computer science, however, concentrated on the ....

J.P. Burgess. Basic tense logic. In D. Gabbay, , and F. Guenther, editors, Handbook of Philosophical Logic, Vol. II, pages 89-134. Reidel, 1984.

....from these automata to LTL using results from [Wil99a] computation tree, and that temporal logic is a logic for describing properties of this tree. In classical temporal logic, this is referred to as unpreventability of the past and leads to so called Ockhamist temporal logics [Pri67, Bur84] Logics with a branching past do not adhere to this view and really talk about something other than the behavior, most often the internal structure of the system . Syntactically, one de nes PCTL # , or CTL # Past , with the following grammar: #, # : # S # usual CTL # syntax (PCTL ....

J. P. Burgess. Basic tense logic. In D. M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. II: Extensions of Classical Logic, chapter 2, pages 89133. D. Reidel Publishing, 1984.

.... in ordinary modal logic) Despite the undefinability of Antisymmetry, we can prove a completeness result for the class of antisymmetric two sorted frames: we will now show that MTL 0 is complete with respect to such frames; we use a technique based on Burgess chronicle construction (cf. Burgess [2]) Definition 2.3 Below we write ; ff for the canonical displacement relation defined in the proof of Theorem 2.1: Sigma ; ff Gamma if for all fl 2 Gamma , Delta ff fl 2 Sigma . Let F = T ; D; DIS) be a two sorted frame, and g an interpretation of the algebraic terms on F. A chronicle on ....

....the spatial behavior of read and write heads of a hard disk. Developing this more liberal approach to interpreting metric temporal languages is part of our ongoing research. In this paper we have not discussed decidability issues. It is known that a negative result holds for Q MTL 0 . Burgess [2] shows that the decision problem for quantified metric temporal logic is equivalent to that for the set of all universal monadic second order formulae true in all ordered abelian groups, and he proves that the decision problem for the validity of firstorder formulae involving a single binary ....

J.P. Burgess. Basic tense logic. In: [5], pages 89--134.

....important, in many cases decision algorithms for automated verification can be obtained from the completeness proofs. Deductions in Multimodal Logic To illustrate the basic idea, we start with a deductive system for multimodal logic for natural models. A number of similar proofs can be found in [2]. We use the following axioms and rules: taut) propositional tautologies (MP) p, p q) q (N) q [a]q (K) a]p A [a] p q) a]q (u) a)q [a]q (L) k (a)q [b] q for a b To prove E) k we have to give a derivation of from the assumptions E) i.e. a sequence of formulas such that the ....

J P Burgess. 'Basic tense logic'. In D Gabbay and F Guenthner, eds., Handbook of philosophical logic, Vol. II, chapter 2, pp. 89-134. Reidel, Dordrecht, (1984).

....function can not. We have already considered some linear time structures other than ( such as the first order theory of the reals under addition. Within linear time logic past time operators have been considered extensively. 1. It is the setting generally considered in Tense Logic (c.f. [7]) 2. Expressive completeness results for F(fl; U) extend to the language with also the past time versions previous and since with respect to the firstorder theory of the integers [32] 3. Vardi [57] considers the linear time calculus with previous , but interpreted over . This language ....

J. P. Burgess. Basic tense logic. In Handbook of Philosophical Logic, Vol. II (D. Gabbay and F. Guenthner (eds.)), pages 89--134, 1984.

....# is open. Say x O. Then x #O, while also x #O (as x #(O O # ) that is, x is a boundary point of O. See Figure 6.b for an illustration. Thus, our x must satisfy q t. Aiello, 2002a] contains a a more sustained analysis of the spatial content of the IR complete Until logic of [Burgess, 1984], with an auxiliary operator G: Gp pU# Here is the set of axioms: G(p ( rUp) rUq) pUr) qUr) 3) rUq) rU(q (rSp) 4) qUp) qUp) Up) qU(q (qUp) 5) # (rUp) # qU(p # r) 6) sUr) q r) s) s)U(q r) 7) For now, ....

Burgess, J. (1984). Basic tense logic. In Gabbay, D. and Guenthner, F., editors, Handbook of Philosophical Logic, volume II, chapter 2, pages 89--133. Reidel.

....temporal logic This is a brief survey of most of the traditional topics and systems of temporal logic in the classical Priorian framework. There are numerous technical and philosophical studies of these logics. For more details on results mentioned here, further references, and much more see [Bur84] BS84] GHR94] GHR95] Gol92] BdRVar] 2.1 Prior s modal framework for temporal logic 2.1.1 Syntax and semantics The basic temporal language L t is a propositional bimodal language, consisting of: the Booleans #, #, the temporal operators G, H, and a set of atomic propositions AT= p ....

J.P. Burgess. Basic tense logic. In Gabbay and Guenthner [GG84], pages 89--133.

....basic multi modal logic Km by means of taking the closure under forming (1) Boolean combinations of accessibility relations (2) the converse of accessibility relations, and (3) the identity relation. All those ingredients have been investigated and applied intensively: see [11, 17, 20] for (1) [5, 12, 30] for (2) and [6] for (3) Hence L can certainly be regarded as a standard member of the modal family. The usefulness of our result, i.e. the expressive completeness of L for FO 2 , is demonstrated by showing that it provides a general framework for comparing the expressive power and ....

....for the two variable fragment over K. It is not hard to see that any ML(S) formula can be translated into an equivalent ML(fR;R g) formula 0 whose length is linear in the length of . In other words, the language of temporal logic with operators always in the future and always in the past [5, 12] is expressively complete for the two variable fragment over any class of strict linear orderings. ii) Consider again a class K of strict linear orderings hW; Ri. Let, for every F = hW; Ri 2 K, Int(F) hI(F) R 1 ; R 13 i, where I(F) is the set of intervals in F and R 1 ; R 13 ....

J.P. Burgess. Basic tense logic. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 89-133. Reidel, Dordrecht, 1984.

....operators on roles, 16] for Boolean operators on roles and inverse roles, and [6] for (some) Boolean operators on roles, inverse, and the identity role. Moreover, the modal logic equivalent of L is also a standard modal logic; see, e.g. 11, 15, 19] for Boolean operators on modal parameters, [4, 12, 26] for converse, and [7] for the identity relation. Thus L is the positive answer to the above question for description and modal logics. What kind of description logic is L The expressive power provided by the strong role forming operators in L is demonstrated by the following three examples: 1. ....

J.P. Burgess. Basic tense logic. In Handbook of Philosophical Logic, volume 2, pages 89--133. Reidel, Dordrecht, 1984.

....basic multi modal logic Km by means of taking the closure under forming (1) Boolean combinations of accessibility relations (2) the converse of accessibility relations, and (3) the identity relation. All those ingredients have been investigated and applied intensively: see [11, 17, 20] for (1) [5, 12, 30] for (2) and [6] for (3) so that L can certainly be regarded as a standard member of the modal family. The usefulness of our result, i.e. the expressive completeness of L for FO 2 , is demonstrated by showing that it provides a general framework for comparing the expressive power and ....

....fragment over K. It is not hard to see that any ML(S) formula can be translated into an equivalent ML(fR;R Gamma g) formula 0 whose length is linear in the length of . In other words, the language of temporal logic with operators always in the future and always in the past [5, 12] is expressively complete for the two variable fragment over any class of strict linear orderings. ii) Consider again a class K of strict linear orderings hW; Ri. Let, for every F = hW; Ri 2 K, Int(F) hI(F) R 1 ; R 13 i ; where I(F) is the set of intervals in F and R 1 ; R ....

J.P. Burgess. Basic tense logic. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 89--133. Reidel, Dordrecht, 1984.

....means that from the viewpoint of conditional or entailment, the truth preserving property of reasoning based on CML is meaningless. 775 Temporal classical logic was established in order to deal with those propositions whose truth values may depend on time and to underlie temporal reasoning [3, 13, 14, 19]. As a conservative extension of CML, its has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [10, 15 17] Until recently, various temporal logics have been used in information systems as formal specification, proof, query, and integrity ....

J. P. Burgess, "Basic Tense Logic," in D. Gabbay and F. Guenthner (eds.), "Handbook of Philosophical Logic," Vol. II, pp. 89133, D. Reidel, 1984.

....may depend on time. No account of reasoning can properly be called complete if it does not say something about how we reason about change. Temporal classical logic was established in order to deal with those propositions whose truthvalues may depend on time and to underlie temporal reasoning [12 15]. As a conservative extension of CML, it has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [12 17] For an autonomous evolutionary information system whose behavior changes dynamically, not only truth values of propositions about the ....

.... logic was established in order to deal with those propositions whose truthvalues may depend on time and to underlie temporal reasoning [12 15] As a conservative extension of CML, it has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [12 17]. For an autonomous evolutionary information system whose behavior changes dynamically, not only truth values of propositions about the behavior of the system but also relevant relationships among the propositions may depend on time. Reasoning about the behavior of such a system must be both ....

Burgess J P. Basic Tense Logic. in Gabbay D and Guenthner F (Eds.), Handbook of Philosophical Logic, Vol. II. Dordrecht: D. Reidel, 1984: 89-133.

....operators on roles, 16] for Boolean operators on roles and inverse roles, and [6] for (some) Boolean operators on roles, inverse, and the identity role. Moreover, the modal logic equivalent of L is also a standard modal logic; see, e.g. 11, 15, 19] for Boolean operators on modal parameters, [4, 12, 26] for converse, and [7] for the identity relation. Thus L is the positive answer to the above question for description and modal logics. What kind of description logic is L The expressive power provided by the strong role forming operators in L is demonstrated by the following three examples: 1. ....

J.P. Burgess. Basic tense logic. In Handbook of Philosophical Logic, volume 2, pages 89-133. Reidel, Dordrecht, 1984.

....basic multi modal logic Km by means of taking the closure under forming (1) Boolean combinations of accessibility relations (2) the converse of accessibility relations, and (3) the identity relation. All those ingredients have been investigated and applied intensively: see [11, 17, 20] for (1) [5, 12, 31] for (2) and [6] for (3) Hence L can certainly be regarded as a standard member of the modal family. The usefulness of our result, i.e. the expressive completeness of L for FO 2 , is demonstrated by showing that it provides a general framework for comparing the expressive power and ....

....for the two variable fragment over K. It is not hard to see that any ML(S) formula can be translated into an equivalent ML(fR;R g) formula 0 whose length is linear in the length of . In other words, the language of temporal logic with operators always in the future and always in the past [5, 12] is expressively complete for the two variable fragment over any class of strict linear orderings. ii) Consider again a class K of strict linear orderings hW; Ri. Let, for every F = hW; Ri 2 K, Int(F) hI(F) R 1 ; R 13 i, where I(F) is the set of intervals in F and R 1 ; R 13 ....

J.P. Burgess. Basic tense logic. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 89-133. Reidel, Dordrecht, 1984.

....presented axioms for real time logics, but no true (versus relative) completeness result for dense real time. In [12] completeness results are given for real time logics with ex2 plicit clocks and time bounded operators, but for time modeled by a discrete time domain, the natural numbers. In [9,7], a completeness result is presented for the qualitative (non real time) part of the logics considered in this paper. There, the time domain considered is dense but the hypothesis of finite variability that we consider 1 is dropped and, as a consequence, different techniques have to be applied. ....

....incomplete. Indeed, axiom F5 of [6] is unsound; axiom F7 can be deduced from axiom F8; and the system cannot derive the induction axiom (11) To see this last point, take the structure formed by R 0 followed by R, with finite variability: it satisfies the system of [6] corrected according to [7]) but not the induction axiom. Thus this valid formula cannot be derived in their system. 9 3.2 Quantitative axioms For the real time part, we first describe the static behavior; intersection, union of intervals can be translated into conjunction, disjunction due to the fact that there is a ....

J.P. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume II, pages 89--133. D. Reidel Publishing Company, 1984.

.... (h 0 ) t) j= exp) 8t; h 0 ; h 1 : h 0 h h 1 ( h 0 ; t) j= evexp = h 1 ; di(h 1 ) ffi di Gamma1 (h 0 ) t) j= evexp) 8t; h 0 ; h 1 : h 0 h h 1 ( h 0 ; t) j= p iff (h 1 ; di(h 1 ) ffi di Gamma1 (h 0 ) t) j= p) The proof system for DTL listed in tables 3 and 4 is inspired on [Bur82, Bur84, BKP86, MP89]. An erroneous variant of it appeared in [BKP86] 4 . Furthermore a link with the proof system of [KMP93] is established via axioms Ax7b Ax7f , 4 F5 was not copied correctly. 13 i.e. since these axioms are needed for deriving their proof system. Note: the models of [Bur82, Bur84] need not ....

....Bur84, BKP86, MP89] An erroneous variant of it appeared in [BKP86] 4 . Furthermore a link with the proof system of [KMP93] is established via axioms Ax7b Ax7f , 4 F5 was not copied correctly. 13 i.e. since these axioms are needed for deriving their proof system. Note: the models of [Bur82, Bur84] need not to satisfy the finite variability condition, the persistency conditions (once within an interval going a little bit back or forward doesn t bring you outside that interval) and the induction axiom. This reflects the crucial difference between the model of [KMP93] and ours on the one ....

[Article contains additional citation context not shown here]

J.P. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic., volume II, pages 89--133. Reidel Publishers, 1984.

.... 1 ;di(h 1 )di 1 (h 0 ) t) exp] 8t;h 0 ; h 1 : h 0 q h h 1 (EE (h 0 ;t) evexp] EE (h 1 ;di(h 1 )di 1 (h 0 ) t) evexp] 8t;h 0 ; h 1 : h 0 q h h 1 ( h 0 ; t) j= p iff (h 1 ; di(h 1 ) di 1 (h 0 ) t) j= p) The proof system for DTL listed in tables 3 and 4 is inspired on [Bur82, Bur84, BKP86, KMP93]. Furthermore a link with the proof system of [KMP93] is established via axioms Ax7b Ax7 f , i.e. since these axioms are needed for deriving their proof system. Note: the models of [Bur82, Bur84] need not to satisfy the finite variability condition, the persistence conditions (once within an ....

....1 (h 0 ) t) j= p) The proof system for DTL listed in tables 3 and 4 is inspired on [Bur82, Bur84, BKP86, KMP93] Furthermore a link with the proof system of [KMP93] is established via axioms Ax7b Ax7 f , i.e. since these axioms are needed for deriving their proof system. Note: the models of [Bur82, Bur84] need not to satisfy the finite variability condition, the persistence conditions (once within an interval going a little bit back or forward doesn t bring you outside that interval) and the induction axiom. This reflects the crucial difference between the model of [KMP93] and ours on the one ....

[Article contains additional citation context not shown here]

J.P. Burgess. Basic Tense Logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume II, pages 89--133. Reidel Publishers, 1984.

.... di#erent grades of tense logical involvement [24] Research in philosophy, linguistics, and mathematical logic resulted in a family of (metric) tense logics that take time as a primitive notion and define (timed) states as sets of atomic propositions which are true at given instants, e.g. [6, 13, 14, 25]. In the last year, a few papers demonstrated the possibility of successfully exploiting metric (possibly layered) tense logics in computer science, e.g. 7, 15, 19, 22] On the other hand, most research in computer science concentrated on the so called temporal logics of programs, which have ....

J.P. Burgess. Basic tense logic. In D. Gabbay, , and F. Guenther, editors, Handbook of Philosophical Logic, Vol. II, pages 89--134. Reidel, 1984.

....an NP complete problem. 5. Point based Temporal Description Logics In this Section we present various proposals that extend Description Logics with an explicit point based notion of time following the external approach. The resulting logics are the combination of a static DL with a tense logic [43,13,24]. 5.1. Combining Description and Tense Logics Schild [40] combines the Description Logic ALC with point based modal temporal connectives. The new language is called ALCT , and the temporal connectives are those of tense logic [13] Existential Future (3) Universal Future (2) Next Instant ( ....

....logics are the combination of a static DL with a tense logic [43,13,24] 5.1. Combining Description and Tense Logics Schild [40] combines the Description Logic ALC with point based modal temporal connectives. The new language is called ALCT , and the temporal connectives are those of tense logic [13]: Existential Future (3) Universal Future (2) Next Instant ( Until (U) Re exive Until (U) As in the case of Schmiedel, Bettini, Artale and Franconi s formalisms, the time is part of the semantic structure. A concept denotes a set of pairs of temporal points and individuals ht; ai, while a ....

J.P. Burgess, Basic tense logic, in D.Gabbay and F.Guenther, editors, Handbook of Philosophical Logic, volume 2, pages 89-133. Reidel, Dordrecht, Holland, 1984.

....were present in Prior s 1954 system (Prior 1958) The 1954 system also had a pair of axioms jointly asserting that between any two dates there is another date : FAFFA and PAPPA (ibid) Various other extensions of K t have been investigated. There are surveys in Prior 1967, van Benthem 1983 and Burgess 1984. Each of these empirical axioms can be regarded as advancing a hypothesis involving the earlier than relation (in Prior s notation U or in early papers l ) For example, HAPA asserts that for each moment of time there is an earlier moment; FFAFA and PPAPA between them assert that for ....

....In my view this takes too pessimistic a view of matters (although in the end the issue simply turns on what one is prepared to count as an interesting model of time) TK t is a highly efficient decision procedure for K t . Moreover each of the Prior Scott extensions of K t is known to be decidable (Burgess 1984, sect. 3) The challenge, though, is to find decision procedures for these stronger systems that are efficient enough to be used in a database context. Even when a system is known to be decidable one may, for the sake of computational efficiency, be prepared to put up with an approximate ....

Burgess, J.P. 1984. `Basic Tense Logic'. In Gabbay, D.M., Guenthner, F. (eds) 1984.

....However, for the logics for event structures and csa s, the decidability question remains open. Several attempts have been made to use logics to characterize the behaviour of distributed programs. Temporal modalities have been traditionally interpreted over di erent types of tense structures ([Burgess 1984], Burgess 1980] Using the interleaving approach to modelling concurrency, various authors have used temporal logics de ned on sequences and trees to describe concurrent computations (see e.g. Clarke et al. 1986] Gabbay et al. 1980] Pnueli 1977] Pinter and Wolper have extended 25 this ....

Burgess J P 1984 Basic tense logic, in Gabbay D, Guenthner F (eds.): Handbook of philosophical logic II (Dordrecht: D Reidel) pp. 89-133.

....varies over time. Similarly, modal logics contain operators that allow expressing the possibility or necessity of situations or events. For surveys and introductions of temporal and modal logics in computer science see [25, 83] and in the setting of more traditional philosophical logic see [18, 21, 44, 79]. Propositional mu calculi, the formalisms discussed in the current work, arise in the framework of modal and temporal logics. The distinguishing feature of these languages is explicit minimal and maximal fixpoint operators z and #z.Thetwo main variants considered here are the modal mu calculus ....

Burgess, J. P.: Basic tense logic, in Gabbay, D. & Guenthner, F. (eds.): Handbook of Philosophical Logic, vol. II, Reidel, 1984, pp. 89-113

....Let us mention three basic types of enrichments. The first one extends the language with new particular operators motivated from the specific semantics, e.g. Kamp s binary temporal modalities Since and Until and the more sophisticated Stavi s connectives U 0 (p; q) and S 0 (p; q) see e.g. (Burgess, 1982; Burgess1984) and (Gabbay, 1981b) see the latter as well for a general approach to this type of enrichments of the temporal language) The second one provides the language with new sorts of syntactic objects, constants, restricted variables etc. again naturally arising in the semantic framework. A ....

Burgess J. Basic Tense Logic, in: Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.), Reidel, Dordrecht, vol.II, 1984, 89-133.

....f h 0 and hR g h 0 , thus we have that M H j= hfi hgi[h] But : hfi hgi) 2 h, and as h is an MCS this means hfi hgi 62 h. Thus the straightforward Henkin method won t work, so we ll need to be more delicate. In the following pages I ll show in some detail how a method used by Burgess [6] for various tense logics can be adapted to t L KR . The method is an inductive process which builds something called a chronicle. As we shall see, given a chronicle with certain properties a suitable L KR 28 model lies to hand. It s worth remarking that we re not forced into this chronicle ....

J. Burgess, 1984, Basic Tense Logic, in Handbook of Philosophical Logic, volume 2, edited by D. Gabbay and F. Guenthner, Reidel.

....reference pointers for extended trees CTL rp . Finally, we discuss some open problems and directions for further research. The reader is assumed to have some background in propositional temporal logics (syntax, semantics, deductive systems and completeness theorem) within either of [Ben 91] Bur 84] Gol 87] 1 Preliminaries 1.1 Temporal logic with reference pointers. We consider a propositional temporal language with ffl a set of atomic propositions fp 1 ; p 2 ; g; ffl propositional connectives : and respectively definable ; true) and (false) 2 ffl temporal ....

Burgess J., Basic Tense Logic, in: Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.), Reidel, Dordrecht, vol.II, 1984, 89-133.

....basic types of enrichments. The rst one extends the language with new particular operators intended to express and formalize speci c temporal phenomena, e.g. Kamp s binary temporal modalities Since and Until and the more sophisticated Stavi s connectives U 0 (p; q) and S 0 (p; q) see e.g. [4, 5] and [7] see the latter as well for a general approach to this type of enrichments of the temporal language) The second one provides the language with new sorts of syntactic objects, constants, variables etc. having speci c interpretation in the temporal framework and thus increases generally ....

Burgess J. Basic Tense Logic, in: Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.), Reidel, Dordrecht, vol.II, 1984, 89-133.

....Despite the undefinability of Antisymmetry, we can prove a completeness result for the class of antisymmetric two sorted frames: we will now show that MTL 0 is complete with respect to such frames. To proof this we use a technique which is based on Burgess chronicle construction (see Burgess [2]) Definition 2.3 Below we write ; ff for the canonical displacement relation defined in the proof of Theorem 2.1: Sigma ; ff Gamma if for all fl 2 Gamma , Delta ff fl 2 Sigma . Let F = T ; D; DIS) be a two sorted frame, and g an interpretation of the algebraic terms on F. A chronicle on ....

....(w.r.t. the third argument) ffl Changing the algebraic component. ffl Replacing the abelian group with a semigroup. The complete picture is currently under development. In this report we have not discussed deciability issues. It is known that a negative result holds for Q MTL 0 . Burgess [2] shows that the decision problem for quantified metric temporal logic is equivalent to that for the set of all universal monadic second order formulae true in all ordered abelian groups, and he proves that the decision problem for the validity of first order formulae involving a single binary ....

J.P. Burgess. Basic tense logic. In: [5], pages 89--134.

....may depend on time. No account of reasoning can properly be called complete if it does not say something about how we reason about change. Temporal classical logic was established in order to deal with those propositions whose truth values may depend on time and to underlie temporal reasoning [3, 14, 18]. As a conservative extension of CML, it has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [3, 14 16, 18] For an autonomous evolutionary information system whose behavior changes dynamically, not only truthvalues of propositions about ....

.... was established in order to deal with those propositions whose truth values may depend on time and to underlie temporal reasoning [3, 14, 18] As a conservative extension of CML, it has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [3, 14 16, 18]. For an autonomous evolutionary information system whose behavior changes dynamically, not only truthvalues of propositions about the behavior of the system but also relevant relationships among the propositions may depend on time. Reasoning about the behavior of such a system must be both ....

J. P. Burgess, "Basic Tense Logic," in D. Gabbay and F. Guenthner (eds.), "Handbook of Philosophical Logic," Vol. II, pp. 89-133, D. Reidel, 1984.

....we first write it into the form i (P i ) F i ) where P i is a strictly past time formula and F i is a (non strict) future time formula where past time and future time formulae are defined in Section 2.1.1. It is always possible to write into this past ) future form as it has been shown [Gab79, Bur84, Gab87] that for a temporal logic such as the one that we have described, it is possible to separate an arbitrary formula into an equivalent boolean combination of pure past, present and pure future formulae. This past ) future form can also be achieved by renaming. Renaming allows the ....

J. P. Burgess. Basic Tense Logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic (II), volume 165 of Synthese Library, chapter II.2, pages 89--134. Reidel, 1984.

.... 5) hui(ff fi) oe huiff huifi (T 6) hui(ff fi) j huiff huifi (T 7) 3(ff fi) j 3ff 3fi (T 8) 3(ff fi) oe 3ff 3fi (T 9) 2ff oe [u]2ff (T 10) 2ff oe ff Derived rules (uG) ff (DR1) ff oe fi (DR2) ff oe fi [u]ff huiff oe huifi 3ff oe 3fi The derivations are quite easy (see for instance [Bur]) and hence we omit them. The closure of a formula will play a crucial role in the completeness proof. Definition 2.2 Let ff be a formula. 1. CL 0 (ff) is the least set of formulas containing ff which satisfies: a) If fi 2 CL 0 (ff) then fi 2 CL 0 (ff) b) If fi 1 fi 2 2 CL 0 (ff) then ....

....(T 7) hu Gamma fagiT rue 2 T (s) as well. Then thesis (T 9) gives [u Gamma fag] a]ff 2 T (s) By induction hypothesis, we get [a]ff 2 T (f(u Gamma fag) as required. 2 Now we show that a model can be pulled out from an ff 0 perfect chronicle structure. This technique is due to Burgess [Bur]. 25 Lemma 4.5 Suppose ff 0 is a consistent formula and CH = T S; T ) is ff 0 perfect. Then ff 0 2 DSAT . Proof: Let TS = S; Define TS 0 = S; by ) def = f(s; u; s 0 ) j u V oc; huiT rue 2 T (s) and there is a thin u cube from s to s 0 in TSg Claim : TS 0 is a dts. ....

Burgess, J.P. (1984), Basic tense logic, in "Handbook of philosophical logic, Vol. II," (D. Gabbay and F. Guenthner, Eds.) pp. 89-133, Reidel.

.... different grades of tense logical involvement [Pri67] Research in philosophy, linguistics, and mathematical logic resulted in a family of (metric) tense logics that take time as a primitive notion and define (timed) states as sets of atomic propositions which are true at given instants, e.g. [Bur84,Gab81,Kam68,RU71]. In the last year, a few papers demonstrated the possibility of successfully exploiting metric (possibly layered) tense logics in computer science, e.g. Koy92,Mon96,MdR97] On the other hand, most research in computer science concentrated on the so called temporal logics of programs, which have ....

J.P. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. II, pages 89--133. D. Reidel Pub. Comp., Dordrecht-Holland, 1984.

.... different grades of tense logical involvement [9] Research in philosophy, linguistics, and mathematical logic resulted in a family of (metric) tense logics that take time as a primitive notion and define (timed) states as sets of atomic propositions which are true at given instants, e.g. [3, 10]. In the last year, a few papers demonstrated the possibility of successfully exploiting metric (possibly layered) tense logics in computer science, e.g. 4, 6, 7] On the other hand, most research in computer science concentrated on the so called temporal logics of programs, which have been ....

J.P. Burgess. Basic tense logic. In D. Gabbay, , and F. Guenther, editors, Handbook of Philosophical Logic, Vol. II, pages 89--134. Reidel, 1984.

.... Prior s di erent grades of tense logical involvement [24] Research in philosophy, linguistics, and mathematical logic resulted in a family of (metric) tense logics that take time as a primitive notion and de ne (timed) states as sets of atomic propositions which are true at given instants, e.g. [6, 13, 14, 25]. In the last year, a few papers demonstrated the possibility of successfully exploiting metric (possibly layered) tense logics in computer science, e.g. 7, 15, 19, 22] On the other hand, most research in computer science concentrated on the so called temporal logics of programs, which have been ....

J.P. Burgess. Basic tense logic. In D. Gabbay, , and F. Guenther, editors, Handbook of Philosophical Logic, Vol. II, pages 89-134. Reidel, 1984.

....not well defined. In most of the reported works, time stamps and event based interval stamps are usually used to represent time varying data at both the tuple and attribute levels. As in the recent works of Tuzhilin and Clifford [26] and Gabbay and McBrien [8] we seek the answer in temporal logic [1]: the meaning of a predicate symbol in temporal semantics is a mapping from moments in time to relations over a given universe of discourse. The collection of moments in time is usually a discrete and linearly ordered set with an unbounded future. In our model, a temporal database is modeled by a ....

....that U be finite. The set of temporal databases over U , denoted as DB, is defined as follows: DB = Rel [ n1 [ P(U n ) It is also the case that DB is a complete lattice induced by the ordering relation v. In more technical terms, members of DB are called temporal interpretations [1]. For any given temporal database db 2 DB and an element p of Rel with arity n, the meaning of p in db is given as db(p) 2 [ P(U n ) As complex time varying attributes or (event based) intervals are not employed in the abstract model, time varying relations are in the First Normal Form ....

J. P. Burgess. Basic tense logic. In D. M. Gabbay and F. Guethner, editors, Handbook of Philosophical Logic, Vol. II, pages 89--134. D. Reidel Publishing Company, 1984.

....the proof methods and completeness will become far more complicated than the present case. Third, QML is essentally a kind of intensional logics[14] so it is possible to combine QML with other intensional logics. In particular, we will be interested in the combination of QML with temporal logic [2] and with epistemic logic [15] A logic for reasoning about knowledge and probability have been successful developed by Fagin et al. 10] Therefore, we believe the combination of QML with epistemic logic and with temporal logic will produce more fruitful results due to the intensional feature of ....

Burgess, J.P., Basic tense logic, in Handbook of Philosophical Logic Volume II : Extension of Classical Logic , ( D. Gabbay, and H. Guenthner, Eds.), D. Reidel Publishing Company, 89-133, 1984.

....relationships among the propositions may depend on time. Reasoning about the behavior of such a system must be both temporal and relevant. Temporal classical logic was established in order to deal with those propositions whose truth values may depend on time and to underlie temporal reasoning [3, 15, 27]. As a conservative extension of classical mathematical logic, its has remarkably expanded the uses of logic to reasoning about human (and hence computer) time related activities [18, 20, 21] However, a reasoning based on temporal classical logic is not necessarily relevant. On the other hand, a ....

J. P. Burgess, "Basic Tense Logic," in D. Gabbay and F. Guenthner (eds.), "Handbook of Philosophical Logic," Vol. II, pp. 89-133, D. Reidel, 1984.

No context found.

Burgess J. [1984], Basic tense logic, in F. G. D. Gabbay, ed., `Handbook of Philosophical Logic', Reidel, chapter II. 2, pp. 89-134.

No context found.

J.P. Burgess. Basic tense logic. In Gabbay and Guenthner [GG84], pages 89--133.

No context found.

J. P. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic: Volume II: Extensions of Classical Logic, pages 89--133. Reidel, Dordrecht, 1984.

No context found.

J. P. Burgess. Basic tense logic. In D. M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. II: Extensions of Classical Logic, chapter 2, pages 89-133. D. Reidel Publishing, 1984.

No context found.

J.P. Burgess. Basic tense logic. In Handbook of Philosophical Logic, volume 2, pages 89--133. Reidel, Dordrecht, 1984.

No context found.

Burgess, J. (1984). Basic tense logic. In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume II, pages 89-133. D. Reidel, Dordrecht-Holland.

No context found.

J.P. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Vol. II, pages 89-133. D. Reidel Pub. Comp., Dordrecht-Holland, 1984.

No context found.

Burgess J., Basic Tense Logic, in: Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.), Reidel, Dordrecht, vol.II, 1984, 89-133.

No context found.

John P. Burgess. Basic tense logic. In Gabbay and Gunthner [GG84], pages 89--134.

No context found.

J. Burgess. Basic tense logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 135--165. D. Reidel, 1984.

No context found.

J. Burgess. Basic tense Logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 135--165. D. Reidel, 1984. 48

No context found.

Burgess, John. 1984. `Basic Tense Logic.' In (Gabbay and Guenthner 1984).

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