Principia Logico-Metaphysica (Draft/Excerpt)
... terms of our language are primitive expressions. The other primitive expressions of our language are listed here. In what follows, we use ↵, , as metavariables ranging over all variables and use µ, ⌫ (Greek mu, nu), sometimes with a prime or an index, as metavariables ranging just over primitive ind ...
... terms of our language are primitive expressions. The other primitive expressions of our language are listed here. In what follows, we use ↵, , as metavariables ranging over all variables and use µ, ⌫ (Greek mu, nu), sometimes with a prime or an index, as metavariables ranging just over primitive ind ...
Labeled Natural Deduction for Temporal Logics
... logics originated by using a generalized (bundled ) semantics obtained by allowing restrictions on the set of branches considered. In the literature, labeled natural deduction systems have been proposed for linear-time logics [19, 103] and the branching logic CTL [20, 131], which, given its syntacti ...
... logics originated by using a generalized (bundled ) semantics obtained by allowing restrictions on the set of branches considered. In the literature, labeled natural deduction systems have been proposed for linear-time logics [19, 103] and the branching logic CTL [20, 131], which, given its syntacti ...
5 model theory of modal logic
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and secon ...
... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and secon ...
logic for the mathematical
... Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two might not be easy to determine. Such statements are often called ...
... Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two might not be easy to determine. Such statements are often called ...
a semantic perspective - Institute for Logic, Language and
... combination of basic modal formulas, or (most interesting of all) a formula prefixed by a diamond or a box. There is redundancy in the way we have defined basic modal languages: we don’t need all these boolean connectives as primitives, and it will follow from the satisfaction definition given below ...
... combination of basic modal formulas, or (most interesting of all) a formula prefixed by a diamond or a box. There is redundancy in the way we have defined basic modal languages: we don’t need all these boolean connectives as primitives, and it will follow from the satisfaction definition given below ...
Combinaison des logiques temporelle et déontique pour la
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
x - Loughborough University Intranet
... An example : addition of integers Semantics : the addition of two integers is defined as the cardinal of the union of two relevant discrete collections ; the result is independent of the nature of the involved object (with respect that mixing these objects will preserve their integrity) Syntax : Add ...
... An example : addition of integers Semantics : the addition of two integers is defined as the cardinal of the union of two relevant discrete collections ; the result is independent of the nature of the involved object (with respect that mixing these objects will preserve their integrity) Syntax : Add ...
Acts of Commanding and Changing Obligations
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
Classical first-order predicate logic This is a powerful extension of
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
Predicate logic definitions
... Warning: This is the informal semantics presented in Bergmann et al. Some important details dealt with by the formal semantics are left implicit. ...
... Warning: This is the informal semantics presented in Bergmann et al. Some important details dealt with by the formal semantics are left implicit. ...
A Judgmental Reconstruction of Modal Logic
... explanation of conjunction. We have said that a verification of A ∧ B consists of a verification of A and a verification of B. Local completeness entails that it is always possible to bring the verification of A ∧ B into this form by a local expansion. To summarize, logic is based on the notion of j ...
... explanation of conjunction. We have said that a verification of A ∧ B consists of a verification of A and a verification of B. Local completeness entails that it is always possible to bring the verification of A ∧ B into this form by a local expansion. To summarize, logic is based on the notion of j ...
Provability as a Modal Operator with the models of PA as the Worlds
... Proof: MB has a root at N iff hN, Bi ∈ R for every B ∈ W . Now the set {B: hN, Bi ∈ R} = Mod(PA ∪ {ϕ: A Bϕ}), so MB has a central world A iff Mod(PA) = Mod(PA ∪ {ϕ: A Bϕ}). Now if B is equivalent to PA, then {ϕ: N Bϕ} = Th(PA), then Mod(PA) = Mod(PA ∪ {ϕ: N Bϕ}) and N is central. If on the othe ...
... Proof: MB has a root at N iff hN, Bi ∈ R for every B ∈ W . Now the set {B: hN, Bi ∈ R} = Mod(PA ∪ {ϕ: A Bϕ}), so MB has a central world A iff Mod(PA) = Mod(PA ∪ {ϕ: A Bϕ}). Now if B is equivalent to PA, then {ϕ: N Bϕ} = Th(PA), then Mod(PA) = Mod(PA ∪ {ϕ: N Bϕ}) and N is central. If on the othe ...
CUED PhD and MPhil Thesis Classes
... Substructural logics are logics which omit some structural rules, e.g. contraction, weakening, commutativity. Nonassociative Lambek calulus (NL) introduced by Lambek is a propositional logic omitting all structural rules, which can be treated as a basic core of substructural logics. NL can be enrich ...
... Substructural logics are logics which omit some structural rules, e.g. contraction, weakening, commutativity. Nonassociative Lambek calulus (NL) introduced by Lambek is a propositional logic omitting all structural rules, which can be treated as a basic core of substructural logics. NL can be enrich ...
Logic
... The truth of Q(x), however, depends on the value of x. This is called a propositional function or an open sentence. More than one variable may be present, as in R(x, y ). The truth of this open sentence can only be determined when both x and y are known. ...
... The truth of Q(x), however, depends on the value of x. This is called a propositional function or an open sentence. More than one variable may be present, as in R(x, y ). The truth of this open sentence can only be determined when both x and y are known. ...