a semantic perspective - Institute for Logic, Language and

... formulas in such graphs) and the standard translation (which links modal logic with classical logic). With these preliminaries out of the way, we are ready to go deeper. What can (and cannot) modal languages say about graphs? In Section 3 we introduce the notion of bisimulation and use it to develop ...

... formulas in such graphs) and the standard translation (which links modal logic with classical logic). With these preliminaries out of the way, we are ready to go deeper. What can (and cannot) modal languages say about graphs? In Section 3 we introduce the notion of bisimulation and use it to develop ...

5 model theory of modal logic

... over the given frame (in effect an abstraction through implicit universal second-order quantification over all valuations); this semantics, accordingly, is of essentially secondorder nature. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states ...

... over the given frame (in effect an abstraction through implicit universal second-order quantification over all valuations); this semantics, accordingly, is of essentially secondorder nature. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states ...

Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic

... over the given frame (in eﬀect an abstraction through implicit universal second-order quantiﬁcation over all valuations); this semantics, accordingly, is of essentially secondorder nature. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states ( ...

... over the given frame (in eﬀect an abstraction through implicit universal second-order quantiﬁcation over all valuations); this semantics, accordingly, is of essentially secondorder nature. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states ( ...

Independence logic and tuple existence atoms

... M |=s R~t if and only if ~thsi ∈ R M ; M |=s ¬R~t if and only if ~thsi 6∈ R M ; M |=s t1 = t2 if and only if t1 hsi = t2 hsi; M |=s t1 6= t2 if and only if t1 hsi = t2 hsi; M |=s φ ∧ ψ if and only if M |=s φ and M |=s ψ; M |=s φ ∨ ψ if and only if M |=s φ or M |=s ψ; M |=s ∃xφ if and only if ∃m ∈ Do ...

... M |=s R~t if and only if ~thsi ∈ R M ; M |=s ¬R~t if and only if ~thsi 6∈ R M ; M |=s t1 = t2 if and only if t1 hsi = t2 hsi; M |=s t1 6= t2 if and only if t1 hsi = t2 hsi; M |=s φ ∧ ψ if and only if M |=s φ and M |=s ψ; M |=s φ ∨ ψ if and only if M |=s φ or M |=s ψ; M |=s ∃xφ if and only if ∃m ∈ Do ...

How to Go Nonmonotonic Contents David Makinson

... acting on sets A of formulae to give larger sets Cn(A). In effect, the operation gathers together all the formulae that are consequences of given premises. The two representations of classical consequence are trivially interchangeable. Given a relation |-, we may define the operation Cn by setting C ...

... acting on sets A of formulae to give larger sets Cn(A). In effect, the operation gathers together all the formulae that are consequences of given premises. The two representations of classical consequence are trivially interchangeable. Given a relation |-, we may define the operation Cn by setting C ...

Annals of Pure and Applied Logic Commutative integral bounded

... BL-algebra A equipped with an order reversing involution ∼ such that ε x (where now → means the implication operation in BL-algebras) satisfy certain equations. In particular it is required that ε x be complemented for all x ∈ A. It follows that ε is an interior operator. Remarkably, this coincides ...

... BL-algebra A equipped with an order reversing involution ∼ such that ε x (where now → means the implication operation in BL-algebras) satisfy certain equations. In particular it is required that ε x be complemented for all x ∈ A. It follows that ε is an interior operator. Remarkably, this coincides ...

A joint logic of problems and propositions, a modified BHK

... for example, of geometric construction problems. [...] Thus, in addition to theoretical logic, a certain new calculus of problems arises. [...] Surprisingly, the calculus of problems coincides in form with Brouwer’s intuitionistic logic, as recently formalized by Heyting. [In fact, we shall argue] t ...

... for example, of geometric construction problems. [...] Thus, in addition to theoretical logic, a certain new calculus of problems arises. [...] Surprisingly, the calculus of problems coincides in form with Brouwer’s intuitionistic logic, as recently formalized by Heyting. [In fact, we shall argue] t ...

The Journal of Functional and Logic Programming The MIT Press

... to L, that is, for every c ∈ L, either T |= ∃ The number of instances of CLP(X ) has grown so much in the last years that it would be impractical to cite them all. Classical CLP(X ) systems, so to speak, are CLP(R) [JMSY92], which computes over the constraint domain of linear arithmetic over the rea ...

... to L, that is, for every c ∈ L, either T |= ∃ The number of instances of CLP(X ) has grown so much in the last years that it would be impractical to cite them all. Classical CLP(X ) systems, so to speak, are CLP(R) [JMSY92], which computes over the constraint domain of linear arithmetic over the rea ...

Systematic Verification of the Modal Logic Cube in Isabelle

... In contrast to the monomodal case, in quantified multimodal logics both modalities and ♦ are parametrized, such that they refer to potentially different accessibility relations. We write R and ♦R to refer to necessity and possibility wrt. a relation R. Furthermore, in terms of quantification, we ...

... In contrast to the monomodal case, in quantified multimodal logics both modalities and ♦ are parametrized, such that they refer to potentially different accessibility relations. We write R and ♦R to refer to necessity and possibility wrt. a relation R. Furthermore, in terms of quantification, we ...

Nonmonotonic Reasoning

... as well as many areas of philosophical inquiry. The origins of nonmonotonic reasoning within the broad area of logical AI lied in dissatisfaction with the traditional logical methods in representing and handling the problems posed by AI. Basically, the problem was that reasoning necessary for an int ...

... as well as many areas of philosophical inquiry. The origins of nonmonotonic reasoning within the broad area of logical AI lied in dissatisfaction with the traditional logical methods in representing and handling the problems posed by AI. Basically, the problem was that reasoning necessary for an int ...

Artificial Intelligence Illuminated

... This book is intended for students of computer science at the college level, or students of other subjects that cover Artificial Intelligence. It also is intended to be an interesting and relevant introduction to the subject for other students or individuals who simply have an interest in the subjec ...

... This book is intended for students of computer science at the college level, or students of other subjects that cover Artificial Intelligence. It also is intended to be an interesting and relevant introduction to the subject for other students or individuals who simply have an interest in the subjec ...

Logic Program Based Updates

... in the body of r without weak negation {L1 , · · · , Lm }, and neg(r) the set of literals in the body of r with weak negation in front {Lm+1 , · · · , Ln }. We specify body(r) to be pos(r) ∪ neg(r). We also use head(r) to denote the head of r: {L0 }. Then we use lit(r) to denote head(r) ∪ body(r). B ...

... in the body of r without weak negation {L1 , · · · , Lm }, and neg(r) the set of literals in the body of r with weak negation in front {Lm+1 , · · · , Ln }. We specify body(r) to be pos(r) ∪ neg(r). We also use head(r) to denote the head of r: {L0 }. Then we use lit(r) to denote head(r) ∪ body(r). B ...

# 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.