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| 2. |
- Holenderski, Leszek, et al.
(author)
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Propositional Description of Finite Cause-Effect Structures
- 1988
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In: Information Processing Letters. - : Elsevier. - 0020-0190 .- 1872-6119. ; 27:3, s. 111-117
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Journal article (peer-reviewed)abstract
- An alternative method of describing semantics of cause-effect structures is presented. It is based on a model of discrete dynamic systems. The model is similar to a condition-event Petri net, differing in the way restrictions on the alterability of actions are imposed.
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| 3. |
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| 4. |
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| 5. |
- Szalas, Andrzej
(author)
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A Complete Axiomatic Characterization of First-Order Temporal Logic of Linear Time
- 1987
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In: Theoretical Computer Science. - : Elsevier. - 0304-3975 .- 1879-2294. ; 54:2-3, s. 199-214
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Journal article (peer-reviewed)abstract
- As shown in (Szalas, 1986, 1986, 1987) there is no finitistic and complete axiomatization of First-Order Temporal Logic of linear and discrete time. In this paper we give an infinitary proof system for the logic. We prove that the proof system is sound and complete. We also show that any syntactically consistent temporal theory has a model. As a corollary we obtain that the Downward Theorem of Skolem, Lowenheim and Tarski holds in the case of considered logic.
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| 6. |
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| 7. |
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| 8. |
- Szalas, Andrzej
(author)
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Concerning the Semantic Consequence Relation in First-Order Temporal Logic
- 1986
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In: Theoretical Computer Science. - : Elsevier. - 0304-3975 .- 1879-2294. ; 47:3, s. 329-334
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Journal article (peer-reviewed)abstract
- In this paper we consider the first-order temporal logic with linear and discrete time. We prove that the set of tautologies of this logic is not arithmetical (i.e., it is neither Σ0n nor Π0n for any natural number n). Thus we show that there is no finitistic and complete axiomatization of the considered logic.
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| 9. |
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| 10. |
- Szalas, Andrzej, et al.
(author)
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Incompleteness of First-Order Temporal Logic with Until
- 1988
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In: Theoretical Computer Science. - : Elsevier. - 0304-3975 .- 1879-2294. ; 57:2-3, s. 317-325
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Journal article (peer-reviewed)abstract
- The results presented in this paper concern the axiomatizability problem of first-order temporal logic with linear and discrete time. We show that the logic is incomplete, i.e., it cannot be provided with a finitistic and complete proof system. We show two incompleteness theorems. Although the first one is weaker (it assumes some first-order signature), we decided to present it, for its proof is much simpler and contains an interesting fact that finite sets are characterizable by means of temporal formulas. The second theorem shows that the logic is incomplete independently of any particular signature.
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