CURRICULUM VITAE Academic Education Academic Employment
... 10. Shai Ben-David and Rachel Ben-Eliyahu, "A modal logic for subjective default reasoning'', Artificial Intelligence, volume 116(1-2), pp. 217-236, 2000. 11. Rachel Ben-Eliyahu, “Yet some more complexity results for default logic”, Artificial Intelligence, volume 139(1), pp. 1-20, 2002. 12. F. Angi ...
... 10. Shai Ben-David and Rachel Ben-Eliyahu, "A modal logic for subjective default reasoning'', Artificial Intelligence, volume 116(1-2), pp. 217-236, 2000. 11. Rachel Ben-Eliyahu, “Yet some more complexity results for default logic”, Artificial Intelligence, volume 139(1), pp. 1-20, 2002. 12. F. Angi ...
Many-Valued Models
... The technique of using finite models defined by means of tables (which turns out to be finite algebras) is arguably older than many-valued logics themselves, and has provided much information not only about non-classical systems as relevant logics, linear logic, intuitionistic logics and paraconsist ...
... The technique of using finite models defined by means of tables (which turns out to be finite algebras) is arguably older than many-valued logics themselves, and has provided much information not only about non-classical systems as relevant logics, linear logic, intuitionistic logics and paraconsist ...
Logics of Truth - Project Euclid
... of models for the theory. Moreover, even though the theory is cast within the general setting of classical logic the construction of the models is essentially based on the inductive technique introduced into truth-theory by Kripke [9], and gains its formal credibility through a nonstandard treatment ...
... of models for the theory. Moreover, even though the theory is cast within the general setting of classical logic the construction of the models is essentially based on the inductive technique introduced into truth-theory by Kripke [9], and gains its formal credibility through a nonstandard treatment ...
Systems of modal logic - Department of Computing
... system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilbert systems: given a set of formulas called axioms and a set of rules of proof, a formula A ...
... system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilbert systems: given a set of formulas called axioms and a set of rules of proof, a formula A ...
Knowledge Representation and Reasoning
... approaches for temporal logic programming languages equipped with negation-asfailure [76]. This last line of research – i.e. semantics for negation in Logic Programming – has also been pursued independently by Rondogiannins in [104], as well as in collaboration with other colleagues [106, 107, 24, 7 ...
... approaches for temporal logic programming languages equipped with negation-asfailure [76]. This last line of research – i.e. semantics for negation in Logic Programming – has also been pursued independently by Rondogiannins in [104], as well as in collaboration with other colleagues [106, 107, 24, 7 ...
Sequentiality by Linear Implication and Universal Quantification
... then O M̄ stands for M1 O· · ·OMh . If x̄ = (x|h1 ) ∈ x⋆ then ∀ x̄:M stands for ∀x1 . . . xh :M when h > 0, and for M when h = 0. We adopt a special kind of sequents, made up from collections of methods with different structures imposed on them: sets, multisets and sequences. Sets are used to repres ...
... then O M̄ stands for M1 O· · ·OMh . If x̄ = (x|h1 ) ∈ x⋆ then ∀ x̄:M stands for ∀x1 . . . xh :M when h > 0, and for M when h = 0. We adopt a special kind of sequents, made up from collections of methods with different structures imposed on them: sets, multisets and sequences. Sets are used to repres ...
Complexity of Recursive Normal Default Logic 1. Introduction
... translations, [GL90, MT93, MNR93], to show that this nonmonotonic rule system can also be represented as recursive propositional or a finite predicate logic program with classical negation and a recursive propositional or finite predicate logic normal default theory. We note in passing that the tech ...
... translations, [GL90, MT93, MNR93], to show that this nonmonotonic rule system can also be represented as recursive propositional or a finite predicate logic program with classical negation and a recursive propositional or finite predicate logic normal default theory. We note in passing that the tech ...
S. P. Odintsov “REDUCTIO AD ABSURDUM” AND LUKASIEWICZ`S
... A translation α from the language L1 to the language L2 preserves propositional variables if α(p) = p for any propositional variable p and it preserves an n-ary connective ∗ if ∗ ∈ L1 ∩ L2 and α(∗(ϕ1 , . . . , ϕn )) = ∗(αϕ1 , . . . αϕn ) for all formulae ϕ1 , . . . , ϕn . Now we recall the definition ...
... A translation α from the language L1 to the language L2 preserves propositional variables if α(p) = p for any propositional variable p and it preserves an n-ary connective ∗ if ∗ ∈ L1 ∩ L2 and α(∗(ϕ1 , . . . , ϕn )) = ∗(αϕ1 , . . . αϕn ) for all formulae ϕ1 , . . . , ϕn . Now we recall the definition ...
Concept Hierarchies from a Logical Point of View
... Recall the standard definition of an interpretation within the framework of predicate logic: an interpretation of Σ consists of a universe U and a function that takes each monadic predicate p ∈ Σ to a subset of U . Now observe that a formal context hU, Σ, i uniquely corresponds to an interpretation ...
... Recall the standard definition of an interpretation within the framework of predicate logic: an interpretation of Σ consists of a universe U and a function that takes each monadic predicate p ∈ Σ to a subset of U . Now observe that a formal context hU, Σ, i uniquely corresponds to an interpretation ...
Predicate logic
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
Some Principles of Logic
... • If the premises are true then the conclusion is probably but not necessarily true • The conclusion contains information not present, even implicitly, in the premises ...
... • If the premises are true then the conclusion is probably but not necessarily true • The conclusion contains information not present, even implicitly, in the premises ...
Quantified Equilibrium Logic and the First Order Logic of Here
... This report continues the work of [26] on first-order, or, as we shall say, quantified equilibrium logic (or QEL for short) and its relation to non-ground answer set programming. The report has three main contributions. First, we present a slightly different version of QEL where the so-called unique n ...
... This report continues the work of [26] on first-order, or, as we shall say, quantified equilibrium logic (or QEL for short) and its relation to non-ground answer set programming. The report has three main contributions. First, we present a slightly different version of QEL where the so-called unique n ...
propositions and connectives propositions and connectives
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
Unifying Logical and Statistical AI - Washington
... containing the single formula ∀x R(x) ⇒ S(x) with weight w, and C = {A}. This leads to four possible worlds: {¬R(A), ¬S(A)}, {¬R(A), S(A)}, {R(A), ¬S(A)}, and {R(A), S(A)}. From Equation 3 we obtain that P ({R(A), ¬S(A)}) = 1/(3ew + 1) and the probability of each of the other three worlds is ew /(3e ...
... containing the single formula ∀x R(x) ⇒ S(x) with weight w, and C = {A}. This leads to four possible worlds: {¬R(A), ¬S(A)}, {¬R(A), S(A)}, {R(A), ¬S(A)}, and {R(A), S(A)}. From Equation 3 we obtain that P ({R(A), ¬S(A)}) = 1/(3ew + 1) and the probability of each of the other three worlds is ew /(3e ...
Unification in Propositional Logic
... By exploiting the above mentioned effect of transformations of the kind (θaA)∗ on Kripke models, one can show that a carefully built iteration θA of substitutions of the kind θaA can in fact always act as the contraction transformation of a contractible A∗ (that is, either such θA unifies A and cons ...
... By exploiting the above mentioned effect of transformations of the kind (θaA)∗ on Kripke models, one can show that a carefully built iteration θA of substitutions of the kind θaA can in fact always act as the contraction transformation of a contractible A∗ (that is, either such θA unifies A and cons ...
Proofs as Efficient Programs - Dipartimento di Informatica
... space [19]), etc. Moreover, we now have also systems where, contrary to lal, the soundness for polynomial time holds for lambda-calculus reduction, like dlal [6] and other similar systems. As a result, the general framework of light logics is now full of different systems, and of variants of those s ...
... space [19]), etc. Moreover, we now have also systems where, contrary to lal, the soundness for polynomial time holds for lambda-calculus reduction, like dlal [6] and other similar systems. As a result, the general framework of light logics is now full of different systems, and of variants of those s ...
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.