| 词汇 | example_english_axiom |
| 释义 | Examples of axiomThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. Next, they study and prove some axioms of the virtual fundamental class. The main lexical elements, which the various systems learn, are words and the main ontological elements are concepts, relations and axioms. There is work ongoing to extend it to learn implicit axioms from text too. In this system the explicit axioms in conditional and quantified sentences in input texts are learned. The explanatory frame axioms can also be expressed in terms of the auxiliary variables. Further, state invariant axioms are included that describe the relationships between -uents within a state. Frame axioms are expressed either by classical frame axioms or by explanatory frame axioms. The simulation process is accomplished by deduction with logical axioms, describing abnormal behaviour, and assumed (abnormal) states. Axioms of the form (6)+(9) are now taken as the (abnormality) axioms. Ultimately, this layered metaphor can be extended to check the ontological axioms themselves against another set of axioms, meta-axioms, which could come from another ontology. Foundational theories provide the semantics for the ontology and their axioms serve as a basis for the implementation of competency questions. The use of ontologies (with axioms) within multi-agent systems is a topic that has recently received much attention. The categorically minded reader will recognise these axioms as the unit, multiplication and functoriality axioms for a monad. The axioms from (le1) to (le6) simply add write effects to assertions. Another way to state this fact is to reason syntactically about the axioms. The axioms are of the form h c: s, where s is a sort and c is a constant or a sort. In our example, we add an equality primitive == to the logic, along with some axioms. Note that, in general, a context can be quite complex, namely the proper axioms might be whenever and wherever we want them. There is no cycle because such a cycle must cross some axioms and some -links that is impossible by construction. In this way, type theory can be formalized with a finite number of axioms. We now check that the axioms are valid in this model. Many axioms are still schemes indexed by types. Thus, the propositions of (), the comprehension schemes and extensionality axioms are valid in this model. The last phase will be a second phase where only cuts with axioms remain, which are then eliminated. Often there are models that do not satisfy the axioms 'literally', but in which all observations nevertheless deliver the required results. The reasoning in parts involving trace is deduced from the axioms of trace. Thus, double duplicators and double dischargers can be defined as generalized natural transformations satisfying similar coherence axioms. Evidently, an interpretation of a derivation is determined by its action on the optional axioms. Figure 10 collects the definitions of several classical properties of term rewrite systems, with some generalised to rewriting modulo a set of axioms. We have all the axioms of propositional logic plus the rules specified below. Then (by completeness) it is provable from the wheel axioms. The last three categorical axioms are concerned with symmetries. Before embarking on the proof, we note a few points about the axioms. The first part just requires manipulation of the axioms; the second and third require the first, with induction on m; the fourth requires the third. The axioms for inclusion tell us when a process behaves better than another in a 'may' perspective. We have also proposed a set of axioms stating mutual exclusion. Finally, fairness axioms are required to guarantee a correct collective behaviour. Here that representation is completed, and it is proved that all extra axioms needed are consistent. We have decided to proceed in this way to explore the consequences of the axioms and to show that they provide insight in understanding domains. The rules of the game on axioms and par links are syncronization requirements between processes. The next thing we have to ensure is that - preserves the axioms. However, if we interpret the axioms called 'laws' as stating properties about conceptual entities named 'processes', then such statements are true. In this paper we analyse how different formalisations interpret their proposed mathematical structures and axioms. In this paper we focus on the axioms called 'laws of processes'. The third group of axioms states how the two transformations can interact together. By the way, this is the only possibility, especially in the absence of axioms, which will be the case in ludics. First, the set of axioms is small and uses well-established concepts only. First, we cannot maintain the axioms of the projection operators. Of course, the axioms will give further restrictions of the integral submanifolds of the horizontal distribution. Throughout their lives women passively assimilate various axioms about how they should function within their families. Because our primary emphasis was to ensure communication between humans, we used axioms fairly freely and had low expectations about translation support. The default reasoning approach takes: simpli®cation, and, negation rationale to be axioms, and supports: left logical equivalence, right weakening. The ten axioms listed in (14) suffice to characterize the relevant collection. Difficulty in seeing the applicability of very simple choice axioms in real-life tasks has been amply demonstrated in the decision theory literature. Suppose now that m is a size as defined by these six axioms. We represent these facts as object level axioms. Others can be regarded as axioms of the domain. Also, it was found that extensive use was made of algebraic laws, which involved the introduction of many unproven laws as axioms. Our approach involves compiling the syntax to the domaintheoretic notation, and simplifying the resulting mathematical expression via equality axioms provided for each semantic primitive. As usual, the equational theory follows from these axioms together with the inference rules for replacing equals for equals. There is hope that these axioms and rules may be substantially simpler than the denotational semantics. In order to function as foundation the axioms must be self-grounding. Instead, the proof can be constructed in such a way as to hold true for every object that satisfies the axioms. One may describe the role of axioms here as the subservient one of fixing the range of variables entering into the explicit constructions. The following two lemmas establish that the well-typedness of program rules and equational axioms is preserved by type instances. The axioms characterized by schemata (6) and (7) ensure the equality theory depends only on the syntax. Also, can state both is-a relations between concepts (axioms) and instance-of relations between individuals (resp. couples of individuals) and concepts (resp. roles) (assertions). The local databases, the supervisor and a set of axioms required to gather information from different databases form the amalgam. When considering a signature as a theory with empty sets of axioms, we are not taking into account labeled rewrite rules. Alternative strategies for priority handling can thus be implemented by necessary changes in the set of axioms. We avoid dealing with this encoding, and describe axioms as if programs were already first order terms. In the presence of terminological axioms, this is no longer possible since the finite model property is not guaranteed to hold. The specification of a module is written in the form of a set of axioms stating the required properties of the procedures of the module. The " " direction follows by the foundational axioms of decomposition and irreducibility. The dissolution of faith in a uniform world-order follows from the dissolution of the unified moral position into a bundle of positive legal axioms. They ceased, that is, to regard self-evidence as a defining property of a system's axioms. The fundamental propositions are the branch's axioms (or postulates)9 and the propositions that follow deductively from them are its theorems. Learning axioms (semi-)automatically is an open problem. Of course, if he also accepts the axioms and inference r ules, then he also unconditionally asserts the consequence. A more ambitious and practically necessary approach would be to take into account how particular ontological axioms are mapped as well. We get to weak ex post prioritarianism just by adding the claim that the betterness relation satisfies the axioms of expected utility theory. The arguments individual players seek are fomulated in the axioms briefly mentioned above and which will be developed in more detail below. While one may not be interested in adding choice axioms, the fact that some choice principles are provably false is undesirable. The question is whether these are all axioms of their kind. Thus, the aggregate data can be rationalised under the standard rationality axioms, while individuals constituting the aggregate do not behave rationally. He takes models to be sets of assumptions or axioms and their deductive consequences chosen in order to address particular problems. None of these two axioms says anything about cases when the worst-off are helped at a great cost to the better-off. The other axioms do not even need to be rephrased. As an illustration, consider the following axioms, applied to this context where individuals are described by their labor-income preferences and their earning abilities. How can the axioms of philosophers with opposing ideologies be identical and contradictory at the same time? Interestingly, they demonstrate that no principle is entirely satisfactory in that none satisfy all of these normative axioms. Secondly, if we accept some additional axioms, then the only value function that satisfies them is critical-level utilitarianism. We will now show that these data and axioms together lead to a characterization result. In so doing, an "authoritarian" element inherent in assuming a priori, as it were, choice axioms dependent on complete and transitive preferences, is removed. Traditionally, the axioms of expected utility theory are regarded as criteria of consistency. In our interpretation there is no such simple pairing of informal ideas with axioms. We now introduce the axioms of a size, define the associated relation and prove it to be an equivalence relation. Such a finding would increase confidence in the normative appropriateness of the axioms and/or in their application to a particular problem. An ontology consists of a set of concepts, axioms, and relationships that describes a domain of interest. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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