Elementary Predicates Research Articles

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

A Logical Analysis of the Anselm’s Unum Argumentum (from Proslogion)

Anselm of Cantorbery wrote Proslogion (1077–1078), where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic (1958, 1973). Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs.

Instrumental prepositions and case: Contexts of occurrence and alternations with datives

We will argue that instrumentals are the mirror image of dative/genitive obliques. We propose that both sets of adpositions/cases are elementary predicates, expressing a zonal inclusion (part-whole/possession relation); instrumentals reverse the direction of the relation with respect to datives/genitives. Our claim is that with-type morphemes provide very elementary means of attaching extra participants (themes, initiators, etc.) to events (VP or vP predicates) – with specialized interpretations derived by pragmatic enrichment (contextual, encyclopedic) at the C-I interface. We will extend our proposal to account for the observation that the instrumentals can be employed cross-linguistically in triadic verb constructions alternating with datives and we will broaden our discussion to account for dative/instrumental syncretism (eventually including DOM objects), arguing that the inclusion predicate (⊆) corresponding to ‘to’ or dative case and its reverse (⊇), corresponding to ‘with’ or instrumental case, may reduce to an even more primitive content capable of conveying inclusion in either direction. Finally, we will address ergative alignments, showing that languages may attach external arguments/agents either as possessors (⊆) or as causers (⊇) of a given event/state, yielding the two most widespread patterns of syncretism of the ergative morpheme, that is with either instrumentals or genitives/datives.

Goal and DOM datives

In a range of Indo-European languages (Romance, Albanian, Iranian, Indo-Aryan), the same oblique case (‘dative’) is associated with indirect objects and with animate/definite direct objects, independently of the particular morphology employed to spell out the oblique (inflectional or pre/postpositional). We argue that there is a syntactic category dative coinciding with the morphological one and encompassing both goal dative and definiteness/animacy dative. We provide a characterization of goal dative as an elementary predicate introducing a part-whole (i.e. possession) relation, arguing that the definiteness/animacy dative is an instance of this elementary predicate. Evidence sometimes used against the unification proposed (e.g. passives, agreement) admits of, or requires, other explanations.

One approach to data analysis in recognition problems on precedents

One approach to data analysis in recognition problems on precedents is investigated. The search task for logical regularities of the classes is considered. The concept of elementary predicate is introduced. This predicate determines the belonging of the object to any half-space in the space of features. The logical regularities, which are the disjunctive forms from elementary predicates, are examined. The search methods for these logical regularities are proposed. These methods are based on the constructing convex hulls of subsets of the training sample.

Logic Program Synthesis as Problem Reduction Using Combining Forms

This paper presents an approach to inductive synthesis of logic programs from examples using problem decomposition and problem reduction principles. This is in contrast to the prevailing logic program induction paradigm, which relies on generalization of programs from examples. The problem reduction is accomplished as a constrained top-down search process, which eventually is to reach trivial problems. Our induction scheme applies a distinguished logic programming language in which programs are combined from elementary predicates by means of combinators conceived of as problem reduction operators including list recursion forms. The operator form admits inductive synthesis as a top-down piecewise composition of semantically meaningful program elements according to the compositional semantics principle and with appeals neither to special generalization mechanisms nor to alternative forms of resolution and unification, or predicate invention. The search space is reduced by subjecting the induction process to various constraints concerning syntactical form, modes, data types, and computational resources. This is illustrated in the paper with well-modedness constraints with the aim of synthesising well-moded, procedurally acceptable programs. Preliminary experiments with the proposed induction method lead us to tentatively conclude that the presented approach forms a viable alternative to the prevailing inductive logic programming methods applying generalization from examples.

DataMine—interactive rule discovery system

DataMine is a statistical database mining system with strong emphasis on interactiveness and nice graphical representation of information produced. It also supports an offline mode of discovery, and provides an extensive API which allows users to write "mining applications" just as easily as routine database applications, The central idea is to perform discovery with a "human in the loop" guiding the system using his initial hypothesis and the feedback from the system. Users can pose a rule-query against a rulebase and the system can generate all rules matching their query. The rulebase could either be pregenerated (using offline mode) or could be realized in real-time as the discovery progresses.Rules generated by the system are of the form: Body -> Consequent where Body is a conjunction of the elementary predicates of the form (A=a), where A is an attribute and a is a value from the attribute domain of A. Consequent is a single elementary predicate. Each rule can have several parameters like support, confidence, atypicality, color etc. (the definitions have been left out) which can also be used by the user in framing the rule query.For continuous attributes, the system also allows the user some control in deciding how they are discretized. It also allows for the creation of extra attributes at run time which can then be used in queries like the rest.

Elementary Functions and LOOP Programs

We study a hierarchy $\{\mathcal{L}_2^k \}$ of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that $n$-place functions in $\mathcal{L}_2^k$ can be enumerated by a single function in $\mathcal{L}_2^{k+2}$, and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are $\mathcal{L}_2^{k+2}$ predicates that are not in $\mathcal{L}_2^{k}$. Along the way the rudimentary predicates of Smullyan are classified as $\mathcal{L}_2^{2}$.

Database inferencing for decision support

The use of databases for management decision support requires flexible inferencing mechanisms. The use of logic programming for these purposes is explored. To be flexible, however, this requires the logical decomposition of the database into elementary predicates.

Life-World Constitution of Propositional Logic and Elementary Predicate Logic

Life-World Constitution of Propositional Logic and Elementary Predicate Logic