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1.
In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment. Mathematics Subject Classification: 03B20, 03B22, 06D15. 相似文献
2.
Yaroslav Shramko 《Annals of Pure and Applied Logic》2021,172(9):103011
This paper presents a Hilbert-style system for the logic of first-degree entailment defined in a Fmla-Fmla framework. The effective use of this formulation as a basis for a whole family of systems extending the logic of first-degree entailment in various directions is shown. By systematizing this family, some new systems are uncovered, and some other well-established logics (such as the first-degree entailment fragment of Priest's Logic of Paradox) obtain new axiomatization. Semantics for the key systems from the family is formulated. 相似文献
3.
Stan J. Surma 《Mathematical Logic Quarterly》1995,41(3):369-372
The paper provides a method for a uniform complete Hilbert-style axiomatisation of Post's (m, u)-conditionals and Post's negation, where m is the number of truth values and u is the number of designated truth values (cf. [5]). The main feature of the technique which we employ in this proof generalises the well-known Kalmár Lemma which was used by its author in his completeness argument for the ordinary, two-valued logic (cf. [2]). 相似文献
4.
Cdric Rivire 《Mathematical Logic Quarterly》2006,52(4):331-339
In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields (more precisely domains) with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable (see also [8]). In this paper we study the case where the fields are expanded with finitely many orderings and an independent derivation. We show that the theory of these fields still admits a model companion in the language L = {+, –, ·, D, <1, …, <m, 1, 0}. We denote this model companion by CODFm and give a geometric axiomatization of this theory which uses basic notions of algebraic geometry and some generalized open subsets which appear naturally in this context. This axiomatization allows to recover (just by putting m = 1) the one given in [4] for the theory CODF of closed ordered differential fields. Most of the technics we use here are already present in [2] and [4]. Finally, we prove that it is possible to describe the completions of CODFm and to obtain quantifier elimination in a slightly enriched (infinite) language. This generalizes van den Dries' results in the “derivation free” case. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Victor Pambuccian 《Mathematical Logic Quarterly》1994,40(4):455-477
In this paper we provide a quantifier-free, constructive axiomatization of metric-Euclidean and of rectangular planes (generalizations of Euclidean planes). The languages in which the axiom systems are expressed contain three individual constants and two ternary operations. We also provide an axiom system in algorithmic logic for finite Euclidean planes, and for several minimal metric-Euclidean planes. The axiom systems proposed will be used in a sequel to this paper to provide ‘the simplest possible’ axiom systems for several fragments of plane Euclidean geometry. Mathematics Subject Classification: 51M05, 51M15, 03F65. 相似文献
6.
We give a complete axiomatization for admissible fragments ofL {ie257-1}(Q). This axiomatization implies syntactically Gregory’s characterization ofL {ie257-2} sentences with no uncountable models ([5]). This is then extended to stationary logic. To obtain these results,
we employ Ressayre’s methods ([16], [17]) augmented with an application of game sentences. In section 4 we prove a result
emphasizing the naturalness of Gregory’s result.
Research supported by a grant from the National Research Council of Canada. 相似文献
7.
Martin Lück 《Annals of Pure and Applied Logic》2018,169(9):928-969
In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(~) of Väänänen's first-order team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas. 相似文献
8.
Bernhard Heinemann 《Mathematical Logic Quarterly》1997,43(2):203-215
Based on a modification of Moss' and Parikh's topological modal language [8], we study a generalization of a weakly expressive fragment of a certain propositional modal logic of time. We define a bimodal logic comprising operators for knowledge and nexttime. These operators are interpreted in binary computation structures. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove – as the main result of this paper – its completeness. Moreover, the question of decidability of T is treated. 相似文献
9.
《Annals of Pure and Applied Logic》2022,173(10):103108
Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level. 相似文献
10.
Esko Turunen 《Mathematical Logic Quarterly》1995,41(2):236-248
A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. 相似文献
11.
A. B. Gordienko 《Algebra and Logic》2007,46(5):289-296
We deal with Sylvan’s logic CCω. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension
of Sylvan’s logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property
of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic
analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.
Supported by RFBR grant No. 06-01-00358 and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 5, pp. 533–547, September–October, 2007. 相似文献
12.
This work deals with the exponential fragment of Girard's linear logic ([3]) without the contraction rule, a logical system which has a natural relation with the direct logic ([10], [7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism ([6]) with respect to the logical system in question. MSC: 03B40, 03F05. 相似文献
13.
Abir Nour 《Mathematical Logic Quarterly》2000,46(3):417-432
In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems the use of a set of constants constitutes a fundamental tool. We have introduced in [8] a logic system called without this kind of constants but limited to the case that T is a finite poset. We have proved a completeness result for this system w.r.t. an algebraic semantics. We introduce in this paper a Kripke‐style semantics for a subsystem of for which there existes a deduction theorem. The set of “possible worldsr is enriched by a family of functions indexed by the elements of T and satisfying some conditions. We prove a completeness result for system with respect to this Kripke semantics and define a finite Kripke structure that characterizes the propositional fragment of logic . We introduce a reational semantics (found by E. Orlowska) which has the advantage to allow an interpretation of the propositionnal logic using only binary relations. We treat also the computational complexity of the satisfiability problem of the propositional fragment of logic . 相似文献
14.
Victor Pambuccian 《Mathematical Logic Quarterly》1994,40(1):76-86
In this paper we provide a quantifier-free constructive axiomatization for Euclidean planes in a first-order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries. Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30. 相似文献
15.
Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability
Viorica Mariela Ungureanu 《Czechoslovak Mathematical Journal》2009,59(2):317-342
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost
problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential
Riccati equation (BDRE) associated with these problems (see [2], for finite dimensional stochastic equations or [21], for
infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [10], [18]).
Under stabilizability and uniform observability conditions and assuming that the control weight-costs are uniformly positive,
we establish that BDRE has a unique, uniformly positive, bounded on ℝ + and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known [18] that uniform
observability does not imply detectability and consequently our results are different from those obtained under detectability
conditions (see [10]).
相似文献
16.
We investigate the consequences of removing the infinitary axiom and rules from a previously defined proof system for a fragment of propositional metric temporal logic over dense time (see [1]). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Edwin D. Mares 《Mathematical Logic Quarterly》1993,39(1):165-177
A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46. 相似文献
18.
Lluís Puig 《Journal of Algebra》2008,319(2):629-656
The purpose of the present paper is two-fold: on the one hand, to show the existence of a correspondence unifying Brauer's and Glauberman's ones (see Theorem 4.6), and, on the other hand, to give an alternative proof of Watanabe's equivalence in [Atumi Watanabe, The Glauberman character correspondence and perfect isometries for blocks of finite groups, J. Algebra 216 (1999) 548–565]. By the way, we give a short proof of the coincidence of the Clifford extensions associated with a pair of Glauberman correspondent irreducible representations (see Corollary 4.16), a question that, surprisingly enough, has only been partially solved recently (see [Morton Harris, Markus Linckelmann, On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups, Trans. Amer. Math. Soc. 354 (2002) 3435–3453] and [Shigeo Koshitani, Gerhard Michler, Glauberman correspondence of p-blocks of finite groups, J. Algebra 243 (2001) 504–517]). 相似文献
19.
Mingsheng Ying 《Mathematical Logic Quarterly》1992,38(1):197-201
In [This Zeitschrift 25 (1979), 45-52, 119-134, 447-464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order Pavelka's logic is preserved under some direct product of lattices of truth values. 相似文献
20.
Frank Wolter 《Mathematical Logic Quarterly》1996,42(1):481-500
Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic
- has the finite model property,
- is complete with respect to Kripke semantics,
- is strongly complete with respect to Kripke semantics,
- is d-persistent,
- is r-persistent.