0-subsumption

A program (hypothesis) is a finite set of definite clauses. The program search space is ordered by a clause subsumption relation, a particular case of generalization and an extension of Plotkin s 0-subsumption. This allows intelligent pruning of the search space, and thus an improvement over basic identification-by-enumeration ... 

This definition is different from classical 0-subsumption for clauses [Plotkin 70], because the used substitution is here given, rather than only constrained to exist. This variant is useful for comparing sets of clauses, as captured in the next definition. 

The concept of 0-subsumption was picked up again by [Shapiro 82], who only considers definite clauses. His search for hypotheses goes from general-to-specific. 

All four components of antireductionism are daunted by at least some of the same problems that vex reductionism the lack of laws in functional biology and the problems in facing a nomic subsumption-account of explanation. If there are no laws and/or explanation is not a matter of subsumption, then antireductionism is false too. However, besides the... 

This is related to the spiritual alienation of the worker who is subjectively or objectively impoverished by what Marx calls "his real subsumption under capital". In early capitalism the worker is only formally subsumed under capital, that is dominated by capital only in the sense of being exploited by capital. This is in one sense the fundamental form of capitalist domination, since it is what makes the real subsumption possible. What goes on "at the point of exchange" between labour and capital determines what goes on "at the point of production" (4.1,5). Yet subjectively or phenomenologically the loss of control over the production process whereby the worker is turned from a producer into a mere instru-mentum vocale may be as intolerable as the fact of being exploited. The... 

The freedom of the consumer is a permanent feature of capitalism. A similar freedom of the worker as producer is limited to the stage of merely formal subsumption of labour under capital, that is the putting-out system and similar arrangements under which the producer works for a... 

This form intensifies the exploitation of the producers, and drives it to an extreme. (The usurer) thus introduces a capitalist mc eof production-albeit to begin with only in the form of the formal subsumption of labour under capital - without doing anything to foster the intensified productivity of labour associated with it or the transition to the capitalist mode of production proper. It Is rather a form which makes labour sterile. ... 

Merchant capital leads to putting-out as a transitional form to capitalism. The producers own some of their means of production, but the merchant provides them with raw materials and buys their product at an agreed price. As with exploitation through usurer s capital, this is neither a real subsumption of labour under capital, corresponding to a change in technique, nor even a formal subsumption. And, as in that case, although... 

For the equivalence of production of relative surplus-value and the specifically capitalist mcxle of production, see Capital f, p. 510. For the equivalence of real subsumption of labour under capital and the specifically capitalist mode of production, see Capital t. p. 738 and Zur Kritik(i 6i 6)>. p. 2145. The equivalence of formjd subsumption and production of absolute surplus-value is asserted in Zur Kritik p, 2130 and in Resu/ls of lltt... 

Immediate Process of Production, p. 1021. In the 1861-3 Critique he also states the contrast between formal and real subsumption as one of "Gegensaiz" or "Enifremdung" vs "Widerspruch" or "Feindlichkelt" (pp. 2014, 2037 ). 

A passage suggesting a similar iriew was cited in 5.1.1. It is also predominant in the discussion of formal subsumption in Results of the Immediate Process of Production and in the 1861-3 Critique. From the latter, the following passage stands out as an explicit affirmation of the two-way causal relationship between the change in the relations of production and the change in the (material) mode of production ... 

With the real subsumption of labour under capital all the changes which we have set out enter into the technological process, the labour process. At the same time there are concomitant changes in the worker s rdation to his own production and to capital. And finally there is a change in the productive power of labour, since... 

The claim that the needs and means of production "coerce" the relations of production into the capitalist mould remains obscure. It certainly cannot mean that capitalism is necessary for the further development of the productive forces. This, while no doubt part of Marx s view, does not enter into his explanation of the rise of capitalism - except at the level of general theory, as in the 1859 Preface. In the more detailed discussions of the emergence of capitalism, he argues that the real subsumption of labour under capital, with the concomitant development of the productive forces, was a mere, non-explanatory by-product of the process. Later, I suggest an interpretation of the first part of the passage, where Marx says that the introduction of capitalism is possible only at a certain level of social production. Here I emphasize the latter part, which leaves little doubt that the emergence of capitalist relations occurred prior to, and independently of, the development of the productive forces. 

S-Match takes two trees as input and provides for any pair of nodes from the two trees the strongest semantic relation that holds between concepts. A lattice of relationship strength is introduced in Giunchiglia et al. [2005], where for example, equivalence is considered stronger than subsumption. This is performed in four stages, the first two can be performed once for each schema, while the last two are performed whenever two schemas are matched. 

The fourth step takes all pairs of nodes and computes a semantic relationship matrix based on the positioning of nodes within their own ontologies. Semantic relations are translated into propositional connectives, with equivalence being translated into equivalence, subsumption into implication, and disjointness into negation. Then, the following formula is checked for satisfiability ... 

Semantic attribute correspondences can be modeled using the similarity matrix model (see Sect. 2). Each ontological relationship is modeled as a separate matrix (one matrix for equivalence, one for subsumption, etc.). These matrices represent the confidence level in an ontological relationships, as generated in the first two... 

Subsumption - two rules have the same conclusion, but the antecedent(s) of one is contained within the other, e.g. 

OWL DL is an expressive language that is a fragment of FOL. This means that it is amenable to machine reasoning. Ontologies described in OWL DL can be checked for logical consistency and subsumption hierarchies (the lattice of is-a links) inferred from the descriptions of classes formed from the links made between classes [20,24,25]. This form of OWL is the focus of this section. 

The approach of organizing objects into classes gives rise to another distinctive feature of object-oriented approaches, viz., inheritance, by which is meant a subsumption relationship between the extents of two classes C and C. Thus, a class C is said to extend (or specialize, or inherit from) a class C if all objects in the extent of C have the same properties, relationships, and compatible method specifications as (but possibly more than) the objects in the extent of C. In this case, C is said to be a subclass of C. Thus, inheritance in object-oriented data models is both structural and behavioral (but the compatibility constraints for the latter are beyond the scope of this discussion). There are many motivations for inheritance mechanisms as described, including a stimulus to reuse, a more direct correspondence with how applications are conceptualized, etc. 

That is what one would expect on a nomic subsumption theory of causation. On such a theory it is natural to view causal locutions as promissory notes singular causal statements that contain them will entail that there is a law covering the events in question without entailing what the law is (Davidson, 1980). The promissory notes should all be cashed out by the time we arrive at fundamental laws. 

Nor is the issue that separates them whether causation analytically requires such oomph factors. Kim does not maintain that causation analytically requires transference. Nomic subsumption and counterfactual theories of causation are offered as analyses of our concept of causation, as statements of noncircular conditions that are individually necessary and jointly sufficient for causation. In contrast, transference theorists typically do not purport to be offering that kind of conceptual analysis. That causation does not analytically require such oomph factors is common ground between Kim and Loewer. 

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