A knowledge-based system under uncertainties and/or incompleteness, referred to as augmented knowledge base (AKB) is provided, including constructing, reasoning, analyzing and applying AKBs by creating objects in the form E→A, where A is a rule in a knowledgebase and E is a set of evidences that supports the rule A. A reasoning scheme under uncertainties and/or incompleteness is provided as augmented reasoning (AR).
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method, comprising: executing, by at least one processor, instructions stored in at least one memory coupled to the at least one processor to: create objects in form E→A from information indicating a knowledge base storing a mapping of values to sets of evidences U, where A is a rule among rules in the knowledge base, and E is a subset of the sets of evidences U from the knowledge base that supports the rule A, so that the rule A is supportable by the subset of evidences E; obtain relationship constraints κ in form of set relations among a plurality of subsets of evidences E; compute for a target rule L, a first composite object with respect to validity (v), ω1v=G1→L0, and/or with respect to plausibility (p), ω1ip=G1→L0, the first composite object ω1v or ω1p constructed from a combination of the objects E→A to create a composite sets of evidences G1v or G1p subject to the relationship constraints κ which support a composite rule L0v or L0p, the composite rule L0v or L0p being a combination of the rules implying the target rule L according to deductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1v or ω1p indicative according to the deductive reasoning of a first validity value or a first plausibility value for the target rule L; compute for at least one target rule L, a first composite object with respect to i-validity (v), ω1iv=G1→L0, and/or with respect to i-plausibility (p), ω1ip=G1→L0, the first composite object ω1iv or ω1ip constructed from a combination of the objects E→A to create a composite sets of evidences G1iv or G1ip subject to the relationship constraints κ which support a composite rule L0iv or L0ip, the composite rule L0iv or L0ip being a combination of the rules implied by the target rule L according to inductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1iv or ω1ip indicative according to the inductive reasoning of a first i-validity value or a first i-plausibility value for the target rule L. 2. The method according to claim 1, wherein: the mapping of the values to the sets of evidences U is according to at least one measure, the at least one measure is at least one function or at least one mapping indicative of a strength of the first i-validity value or the first i-plausibility value for the target rule L with respect to inductive reasoning; and the computed first composite object with respect to validity ω1iv includes computing the first i-validity value by determining a value of the G1iv using the mapped values of the plurality of subsets of evidences E, the first i-validity value indicative of the strength of i-validity for the target rule L according to the measure, or the computed first composite object with respect to validity ω1ip includes computing the first i-plausibility value by determining a value of the G1ip using the mapped values of the plurality of subsets of evidences E, the first i-plausibility value indicative of the strength of i-plausibility for the target rule L according to the measure. 3. The method according to claim 1, wherein the executing by the at least one processor the instructions further causes the at least one processor to: create a new knowledge base by transforming, for each object ω=E→L in the knowledge base, L into conjunctive normal form and include in the new knowledge base each E→Li where Li is a disjunction in L. 4. The method according to claim 1, wherein the at least one target rule L includes rules L1 and L2, and the executing by the at least one processor the instructions further causes the at least one processor to: estimate the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being a subset of union of validity of L1 and validity of L2; validity of a conjunction L1L2 being an intersection of validity of L1 and validity of L2; a plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and a plausibility of a conjunction L1L2 being a subset of an intersection of plausibility of L1 and plausibility of L2. 5. The method according to claim 1, wherein the at least one target rule L includes rules L1 and L2, and the executing by the at least one processor the instructions further causes the at least one processor to: determine, in response to the knowledge base being consistent, the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being union of validity of L1 and validity of L2; validity of a conjunction L1L2 being intersection of validity of L1 and validity of L2; plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and plausibility of a conjunction L1L2 being an intersection of plausibility of L1 and plausibility of L2. 6. An apparatus, comprising: at least one processor; and at least one memory to store instructions which when executed by the at least one processor cause the apparatus to: create objects in form E→A from information indicating a knowledge base storing a mapping of values to sets of evidences U, where A is a rule among rules in the knowledge base, and E is a subset of the sets of evidences U from the knowledge base that supports the rule A, so that the rule A is supportable by the subset of evidences E; obtain relationship constraints κ in form of set relations among a plurality of subsets of evidences E; compute for a target rule L, a first composite object with respect to validity (v), ω1v=G1→L0, and/or with respect to plausibility (p), ω1p=G1→L0, the first composite object ω1v or ω1p constructed from a combination of the objects E→A to create a composite sets of evidences G1v or G1p subject to the relationship constraints κ which support a composite rule L0v or L0p, the composite rule L0v or L0p being a combination of the rules implying the target rule L according to deductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1v or ω1p indicative according to the deductive reasoning of a first validity value or a first plausibility value for the target rule L; compute for at least one target rule L, a first composite object with respect to i-validity (v), ω1iv=G1→L0, and/or with respect to i-plausibility (p), ω1ip=G1→L0, the first composite object ω1iv or ω1ip constructed from a combination of the objects E→A to create a composite sets of evidences G1iv or G1ip subject to the relationship constraints κ which support a composite rule L0iv or L0ip, the composite rule L0iv or L0ip being a combination of the rules implied by the target rule L according to inductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1iv or ω1ip indicative according to the inductive reasoning of a first i-validity value or a first i-plausibility value for the target rule L. 7. The apparatus according to claim 6, wherein: the mapping of the values to the sets of evidences U is according to at least one measure, the at least one measure is at least one function or at least one mapping indicative of a strength of the first i-validity value or the first i-plausibility value for the target rule L with respect to inductive reasoning; and the computed first composite object with respect to validity ω1iv includes computing the first i-validity value by determining a value of the G1iv using the mapped values of the plurality of subsets of evidences E, the first i-validity value indicative of the strength of i-validity for the target rule L according to the measure, or the computed first composite object with respect to validity ω1ip includes computing the first i-plausibility value by determining a value of the G1ip using the mapped values of the plurality of subsets of evidences E, the first i-plausibility value indicative of the strength of i-plausibility for the target rule L according to the measure. 8. The apparatus according to claim 6, wherein the instructions further cause the at least one processor to: create a new knowledge base by transforming, for each object ω=E→L in the knowledge base, L into conjunctive normal form and include in the new knowledge base each E→Li where Li is a disjunction in L. 9. The apparatus according to claim 6, wherein the at least one target rule L includes rules L1 and L2, and the instruction further cause the at least one processor to: estimate the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being a subset of union of validity of L1 and validity of L2; validity of a conjunction L1L2 being an intersection of validity of L1 and validity of L2; a plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and a plausibility of a conjunction L1L2 being a subset of an intersection of plausibility of L1 and plausibility of L2. 10. The apparatus according to claim 6, wherein the at least one target rule L includes rules L1 and L2, and the instructions further cause the at least one processor to: determine, in response to the knowledge base being consistent, the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being union of validity of L1 and validity of L2; validity of a conjunction L1L2 being intersection of validity of L1 and validity of L2; plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and plausibility of a conjunction L1L2 being an intersection of plausibility of L1 and plausibility of L2. 11. At least one server, comprising: at least one processor; and at least one non-transitory computer readable storage medium configured to store: a mapping of values to sets of evidences U in a knowledge base, and objects in the form E→A, where A is a rule among rules in the knowledge base, and E is a subset of the sets of evidences U from the knowledge base that supports the rule A, so that the rule A is supportable by the subset of evidences E; and instructions which when executed by the at least one processor cause the at least one server to: obtain relationship constraints κ in form of set relations among a plurality of subsets of evidences E; compute for a target rule L, a first composite object with respect to validity (v), ω1v=G1→L0, and/or with respect to plausibility (p), ω1p=G1→L0, the first composite object ω1v or ω1p constructed from a combination of the objects E→A to create a composite sets of evidences G1v or G1p subject to the relationship constraints κ which support a composite rule L0v or L0p, the composite rule L0v or L0p being a combination of the rules implying the target rule L according to deductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1v or ω1p indicative according to the deductive reasoning of a first validity value or a first plausibility value for the target rule L; compute for at least one target rule L, a first composite object with respect to i-validity (v), ω1iv=G1→L0, and/or with respect to i-plausibility (p), ω1ip=G1→L0, the first composite object ω1iv or ω1ip constructed from a combination of the objects E→A to create a composite sets of evidences G1iv or G1ip subject to the relationship constraints κ which support a composite rule L0iv or L0ip, the composite rule L0iv or L0ip being a combination of the rules implied by the target rule L according to inductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1iv or ω1ip indicative according to the inductive reasoning of a first i-validity value or a first i-plausibility value for the target rule L. 12. The at least one server according to claim 11, wherein: the mapping of the values to the sets of evidences U is according to at least one measure, the at least one measure is at least one function or at least one mapping indicative of a strength of the first i-validity value or the first i-plausibility value for the target rule L with respect to inductive reasoning; and the computed first composite object with respect to validity ω1iv includes computing the first i-validity value by determining a value of the G1iv using the mapped values of the plurality of subsets of evidences E, the first i-validity value indicative of the strength of i-validity for the target rule L according to the measure, or the computed first composite object with respect to validity ω1ip includes computing the first i-plausibility value by determining a value of the G1ip using the mapped values of the plurality of subsets of evidences E, the first i-plausibility value indicative of the strength of i-plausibility for the target rule L according to the measure. 13. The at least one server according to claim 11, wherein the instructions further cause the at least one processor to: create a new knowledge base by transforming, for each object ω=E→L in the knowledge base, L into conjunctive normal form and include in the new knowledge base each E→Li where Li is a disjunction in L. 14. The at least one server according to claim 11, wherein the at least one target rule L includes rules L1 and L2, and the instructions further cause the at least one processor to: estimate the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being a subset of union of validity of L1 and validity of L2; validity of a conjunction L1L2 being an intersection of validity of L1 and validity of L2; a plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and a plausibility of a conjunction L1L2 being a subset of an intersection of plausibility of L1 and plausibility of L2. 15. The at least one server according to claim 11, wherein the at least one target rule L includes rules L1 and L2, and the instructions further cause the at least one processor to: determine, in response to the knowledge base being consistent, the validity or plausibility of L according to deductive reasoning by repeated applications of decomposition rules including: validity of a disjunction L1L2 being union of validity of L1 and validity of L2; validity of a conjunction L1L2 being intersection of validity of L1 and validity of L2; plausibility of a disjunction L1L2 being a union of plausibility of L1 and plausibility of L2; and plausibility of a conjunction L1L2 being an intersection of plausibility of L1 and plausibility of L2.