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On P/NP Dichotomies for EL Subsumption under Relational Constraints
"... Abstract. We consider the problem of characterising relational constraints under which TBox reasoning in EL is tractable. We obtain P vs. coNPhardness dichotomies for tabular constraints and constraints imposed on a single reflexive role. 1 ..."
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Abstract. We consider the problem of characterising relational constraints under which TBox reasoning in EL is tractable. We obtain P vs. coNPhardness dichotomies for tabular constraints and constraints imposed on a single reflexive role. 1
TRANSITIVE PRIMAL INFON LOGIC
"... Abstract. Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffic ..."
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Abstract. Primal infon logic was introduced in 2009 in connection with access control. In addition to traditional logic constructs, it contains unary connectives p said indispensable in the intended access control applications. Propositional primal infon logic is decidable in linear time, yet suffices for many common access control scenarios. The most obvious limitation on its expressivity is the failure of the transitivity law for implication: x → y and y → z do not necessarily yield x → z. Here we introduce and investigate equiexpressive “transitive ” extensions TPIL and TPIL ∗ of propositional primal infon logic as well as their quotefree fragments TPIL0 and TPIL0 ∗ respectively. We prove the subformula property for TPIL0 ∗ and a similar property for TPIL ∗ ; we define Kripke models for the four logics and prove the corresponding soundnessandcompleteness theorems; we show that, in all these logics, satisfiable formulas have small models; but our main result is a quadratictime derivation algorithm for TPIL ∗. §1. Introduction. In a brickandmortar setting, some access control policies may be vague and even unwritten. The clerks ordinarily know them. When in doubt, they know whom to ask. In the cloud there are no clerks, and policies have to be managed automatically. The most challenging are federated scenarios where the policies of different
Conservativity of Boolean algebras with operators over semilattices with operators
"... problems considered in this paper originate in recent applications of large scale ontologies ..."
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problems considered in this paper originate in recent applications of large scale ontologies
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"... elementarily generated modal logics Abstract. In this paper we consider the normal modal logics of elementary classes defined by firstorder formulas of the form ∀x0∃x1...∃xn∧xiRλxj. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a s ..."
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elementarily generated modal logics Abstract. In this paper we consider the normal modal logics of elementary classes defined by firstorder formulas of the form ∀x0∃x1...∃xn∧xiRλxj. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.