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1.
We introduce non-associative linear logic, which may be seen as the classical version of the non-associative Lambek calculus. We define its sequent calculus, its theory of proof-nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial. 相似文献
2.
3.
A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight. 相似文献
4.
A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML+, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML+ based on the recent results for model checking procedures for temporalised logics. TML+ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML+, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments. 相似文献
5.
Barry Hartley Slater 《Synthese》2008,163(2):187-198
Prawitz proved a theorem, formalising ‘harmony’ in Natural Deduction systems, which showed that, corresponding to any deduction
there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction
rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical
Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can extend the theorem to the classical case. Properly arranged there is a thoroughgoing ‘harmony’, in the classical
rules. Indeed, as we shall see, they are, all together, far more ‘harmonious’ in the general sense than has been commonly
observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural
deduction rules for Classical Logic have been presented. 相似文献
6.
In this paper, we show the weak normalization (WN) of the simply-typedse-calculus with open terms where abstractions are decoratedwith types, and metavariables, de Bruijn indices and updatingoperators are decorated with environments. We show a proof ofWN using the e-calculus, a calculus isomorphic to . This proof is strongly influenced by Goubault-Larrecq'sproof of WN for the -calculus but with subtle differences whichshow that the two styles require different attention. Furthermore,we give a new calculus 'e which works like se but which iscloser to than e. For both e and 'e we prove WN for typedsemi-open terms (i.e. those which allow term variables but nosubstitution variables), unlike the result of Goubault-Larrecqwhich covered all open terms. 相似文献
7.
Stefan Kaufmann 《Journal of Philosophical Logic》2009,38(1):1-53
The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is
a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities
to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines
the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings
intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal
(in)dependence. 相似文献
8.
Norihiro Kamide 《Studia Logica》2009,91(2):217-238
New propositional and first-order paraconsistent logics (called L
ω
and FL
ω
, respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding
theorems of L
ω
and FL
ω
into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple
semantics for L
ω
and FL
ω
are proved. The cut-elimination theorems for L
ω
and FL
ω
are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems.
Presented by Yaroslav Shramko and Heinrich Wansing 相似文献
9.
Phiniki Stouppa 《Studia Logica》2007,85(2):199-214
We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference.
Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity
and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct
design: the rules are few and the modal rules are in exact correspondence to the modal axioms.
Presented by Heinrich Wansing 相似文献
10.
Denis Béchet 《Studia Logica》2007,87(2-3):199-224
The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing
empty premises. 相似文献