On modal logics of group belief
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
LPF and MPLω — A Logical Comparison of VDM SL and COLD-K
... definedness. For formulae formed with Kleene’s or McCarthy’s connectives and Kleene’s quantifiers, logical consequence for three-valued logics according to the second idea reduces to classical logical consequence for two-valued logics. For formulae formed with Kleene’s connectives and Kleene’s quant ...
... definedness. For formulae formed with Kleene’s or McCarthy’s connectives and Kleene’s quantifiers, logical consequence for three-valued logics according to the second idea reduces to classical logical consequence for two-valued logics. For formulae formed with Kleene’s connectives and Kleene’s quant ...
Binary aggregation with integrity constraints Grandi, U. - UvA-DARE
... knowledge SWFs defined on pair judgments have not yet been studied in the literature, and we now prove a possibility result concerning this class of procedures. Proposition 5.2.2. There exists a SWF defined on pair judgments that satisfies the Pareto condition, May’s neutrality, independence and pos ...
... knowledge SWFs defined on pair judgments have not yet been studied in the literature, and we now prove a possibility result concerning this class of procedures. Proposition 5.2.2. There exists a SWF defined on pair judgments that satisfies the Pareto condition, May’s neutrality, independence and pos ...
notes
... implies P . That is, P most accurately describes input states for which c either does not terminate or ends up in a state satisfying Q. Formally, an assertion P is a weakest liberal precondition of c and Q if: ∀σ, I. σ ⊨I P ⇐⇒ (C[[c]] σ) undefined ∨ (C[[c]]σ) ⊨I Q We write wlp(c, Q) for the weakest ...
... implies P . That is, P most accurately describes input states for which c either does not terminate or ends up in a state satisfying Q. Formally, an assertion P is a weakest liberal precondition of c and Q if: ∀σ, I. σ ⊨I P ⇐⇒ (C[[c]] σ) undefined ∨ (C[[c]]σ) ⊨I Q We write wlp(c, Q) for the weakest ...
Propositional Logic
... Conversely, suppose that we have a set of axioms and we wish to know whether the resulting theory (the set of consequences) is consistent, in the sense that no statement and its negation follow from the axioms. If one discovers a structure in which it can be shown that the axioms and their consequen ...
... Conversely, suppose that we have a set of axioms and we wish to know whether the resulting theory (the set of consequences) is consistent, in the sense that no statement and its negation follow from the axioms. If one discovers a structure in which it can be shown that the axioms and their consequen ...
Proof Theory for Propositional Logic
... particular the fact that a conditional is counted as true whenever the antecedent (the first term, above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals f ...
... particular the fact that a conditional is counted as true whenever the antecedent (the first term, above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals f ...
Logic in the Finite - CIS @ UPenn
... What makes the strategy worth pursuing is that there is a powerful, and entertaining, technique, the Ehrenfeucht game, for showing that pairs of structures agree about rst order sentences. This technique applies to both nite and in nite structures and, to some extent, lls the void left by the fa ...
... What makes the strategy worth pursuing is that there is a powerful, and entertaining, technique, the Ehrenfeucht game, for showing that pairs of structures agree about rst order sentences. This technique applies to both nite and in nite structures and, to some extent, lls the void left by the fa ...
Logical Omniscience As Infeasibility - boris
... level of rationality embedded in it: with every known fact, an agent knows all equivalent facts because this semantics is extensional. While seeming perfectly rational, this does smuggle at least some level of logical omniscience: it is not possible for the agent to know simple tautologies but to be ...
... level of rationality embedded in it: with every known fact, an agent knows all equivalent facts because this semantics is extensional. While seeming perfectly rational, this does smuggle at least some level of logical omniscience: it is not possible for the agent to know simple tautologies but to be ...
Godel`s Proof
... and deep the art of mathematical thinking is, and the once-bright hope of mechanizing human mathematical thought starts to seem shaky, if not utterly quixotic. What, then, after Gödel, is mathematical thinking believed to be? What, after Gödel, is mathematical truth? Indeed, what is truth at all? ...
... and deep the art of mathematical thinking is, and the once-bright hope of mechanizing human mathematical thought starts to seem shaky, if not utterly quixotic. What, then, after Gödel, is mathematical thinking believed to be? What, after Gödel, is mathematical truth? Indeed, what is truth at all? ...
Boolean Logic - Programming Systems Lab
... expression is always >, and the prime tree normal form of an unsatisfiable expressions is always ⊥. Thus an expression is satisfiable if and only if its prime tree normal form is different from ⊥. We define prime expressions inductively: 1. ⊥ and > are prime expressions. 2. Cxst is a prime expressi ...
... expression is always >, and the prime tree normal form of an unsatisfiable expressions is always ⊥. Thus an expression is satisfiable if and only if its prime tree normal form is different from ⊥. We define prime expressions inductively: 1. ⊥ and > are prime expressions. 2. Cxst is a prime expressi ...
degrees of recursively saturated models
... Lemma 1.3(i) and (ii), M must realize T(v) by some «. This « codes/,. Similar arguments show that S is closed under joins and has the tree property. Lemma 1.3 also implies M is S-saturated. Suppose that M is also S'-saturated. Then S' G S. Let s' G S'. Coding arguments similar to those above show th ...
... Lemma 1.3(i) and (ii), M must realize T(v) by some «. This « codes/,. Similar arguments show that S is closed under joins and has the tree property. Lemma 1.3 also implies M is S-saturated. Suppose that M is also S'-saturated. Then S' G S. Let s' G S'. Coding arguments similar to those above show th ...
Geometric Modal Logic
... proposition is simply necessary. Speaking of something as ‘possibly possible’, we implicitly let the variation system itself vary, we shift from a given system of possibility into a frame inside which this system is only one among others, and we say that respectively to some other system, such or su ...
... proposition is simply necessary. Speaking of something as ‘possibly possible’, we implicitly let the variation system itself vary, we shift from a given system of possibility into a frame inside which this system is only one among others, and we say that respectively to some other system, such or su ...
PPT
... • An expression’s principal type is the least general type that contains all instances of the expression. • For example, the principal type of head function is [a]->a, while [b] -> a, b -> a, a are correct but too general but [Integer] -> Integer is too ...
... • An expression’s principal type is the least general type that contains all instances of the expression. • For example, the principal type of head function is [a]->a, while [b] -> a, b -> a, a are correct but too general but [Integer] -> Integer is too ...
Continuous Markovian Logic – From Complete ∗ Luca Cardelli
... a-transitions from a given state to the set of states satisfying φ is at least r; similarly, Mra φ states that the rate is at most r. In spite of their syntactic similarities, CML and PML are very different. While in the probabilistic case the two modal operators are dual, being related by the De Mo ...
... a-transitions from a given state to the set of states satisfying φ is at least r; similarly, Mra φ states that the rate is at most r. In spite of their syntactic similarities, CML and PML are very different. While in the probabilistic case the two modal operators are dual, being related by the De Mo ...
Principles of Computer Architecture Dr. Mike Frank
... The Adiabatic Theorem • A result in basic quantum theory – Proved in many quantum mechanics textbooks • Paraphrased: A system initially in its ground state (or more generally, its nth energy eigenstate) will, after subjecting it to a sufficiently slow change of applied forces, remain in the corresp ...
... The Adiabatic Theorem • A result in basic quantum theory – Proved in many quantum mechanics textbooks • Paraphrased: A system initially in its ground state (or more generally, its nth energy eigenstate) will, after subjecting it to a sufficiently slow change of applied forces, remain in the corresp ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.