A System of Interaction and Structure
... admissible rules are in fact independent, and their admissibility can be shown independently by way of splitting. For big logical systems, like linear logic, one can easily get tens of thousands of equivalent systems without much effort [31]. This modularity is ultimately made possible by the top-do ...
... admissible rules are in fact independent, and their admissibility can be shown independently by way of splitting. For big logical systems, like linear logic, one can easily get tens of thousands of equivalent systems without much effort [31]. This modularity is ultimately made possible by the top-do ...
Using linear logic to reason about sequent systems ?
... Consider the well-known, two-sided sequent proof systems for classical, intuitionistic, and linear logic. A convenient distinction between these logics can be described, in part, by where the structural rules of thinning and contraction can be applied. In classical logic, these structural rules are ...
... Consider the well-known, two-sided sequent proof systems for classical, intuitionistic, and linear logic. A convenient distinction between these logics can be described, in part, by where the structural rules of thinning and contraction can be applied. In classical logic, these structural rules are ...
Relevant and Substructural Logics
... and with hypotheses from among the set X. A proof from hypotheses is simply a list of formulas, each of which is either an hypothesis, an axiom, or one which follows from earlier formulas in the list by means of a rule. In Orlov’s system, the only rule is modus ponens. We will see later that this is ...
... and with hypotheses from among the set X. A proof from hypotheses is simply a list of formulas, each of which is either an hypothesis, an axiom, or one which follows from earlier formulas in the list by means of a rule. In Orlov’s system, the only rule is modus ponens. We will see later that this is ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
... empty set. In this case one can conclude ¬Kp for every atom p, but this conclusion does not hold anymore when p is added to I. This idea has been further developed by Lifschitz in [15] and by Lin and Shoham in [17], where a bimodal logic that combines minimization of knowledge with justified assumpt ...
... empty set. In this case one can conclude ¬Kp for every atom p, but this conclusion does not hold anymore when p is added to I. This idea has been further developed by Lifschitz in [15] and by Lin and Shoham in [17], where a bimodal logic that combines minimization of knowledge with justified assumpt ...
Ascribing beliefs to resource bounded agents
... ascribable beliefs to be P = {p1 , ..., pm }. There is a mapping from the state s of the agent to set of propositions it ‘believes’ in: P + (s) assigns some propositions from P as the agent’s positive beliefs, P + (s) ⊆ P. The mapping P − (s) assigns some propositions from P as the agent’s negative ...
... ascribable beliefs to be P = {p1 , ..., pm }. There is a mapping from the state s of the agent to set of propositions it ‘believes’ in: P + (s) assigns some propositions from P as the agent’s positive beliefs, P + (s) ⊆ P. The mapping P − (s) assigns some propositions from P as the agent’s negative ...
Many-Valued Logic
... But this was a dead end. James Dugundji (1940) showed that none of the Lewis modal logics S1-S5 have finite characteristic matrices—meaning, among other things, that they cannot be viewed as many-valued systems with a finite number of truth values. ...
... But this was a dead end. James Dugundji (1940) showed that none of the Lewis modal logics S1-S5 have finite characteristic matrices—meaning, among other things, that they cannot be viewed as many-valued systems with a finite number of truth values. ...
Strong Interactions
... of symmetric wave functions Problem: Δ++ is made out of 3 u quarks, and has spin J=3/2 (= 3 quarks of s= ½ in same state?) This is forbidden by Fermi statistics (Pauli principle)! Solution: there is a new internal degree of freedom (colour) which differentiate the quarks: Δ++=urugub • This means th ...
... of symmetric wave functions Problem: Δ++ is made out of 3 u quarks, and has spin J=3/2 (= 3 quarks of s= ½ in same state?) This is forbidden by Fermi statistics (Pauli principle)! Solution: there is a new internal degree of freedom (colour) which differentiate the quarks: Δ++=urugub • This means th ...
- Free Documents
... By the completeness of L noninterderivable and give rise to distinct and n . This is in general not so for theories. An example is the theory axiomatized by p on the one hand, and the theory T axiomatized by m p for each m, on the other. The sets p and T are the same, consisting of all nodes that to ...
... By the completeness of L noninterderivable and give rise to distinct and n . This is in general not so for theories. An example is the theory axiomatized by p on the one hand, and the theory T axiomatized by m p for each m, on the other. The sets p and T are the same, consisting of all nodes that to ...
The Foundations
... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...
... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...
MODAL LANGUAGES AND BOUNDED FRAGMENTS OF
... Here, a bisimulation is a binary relation between the domains of two first-order models linking points with the same unary predicates P , corresponding to modal proposition letters p , and satisfying two 'back-and-forth' or 'zigzag clauses' with respect to relational R-successors. (More precisely, ...
... Here, a bisimulation is a binary relation between the domains of two first-order models linking points with the same unary predicates P , corresponding to modal proposition letters p , and satisfying two 'back-and-forth' or 'zigzag clauses' with respect to relational R-successors. (More precisely, ...
A Survey on Small Fragments of First-Order Logic over Finite
... ferent characterizations are known than for star-free languages. The algebraic counterpart is the class DA of finite monoids. The first letter D stands for one of Green’s relations [25] and the second letter comes from Aperiodic. Schützenberger has characterized DA by unambiguous polynomials which ...
... ferent characterizations are known than for star-free languages. The algebraic counterpart is the class DA of finite monoids. The first letter D stands for one of Green’s relations [25] and the second letter comes from Aperiodic. Schützenberger has characterized DA by unambiguous polynomials which ...
Chpt-3-Proof - WordPress.com
... • The integer is even if there exists an integer k such that n = 2k. • An is odd if there exists an integer k such that n = 2k+1. • Note: An integer is either even or odd, but not both. • This is an immediate consequence of the division algorithm: If a and b are positive integers, then there exist u ...
... • The integer is even if there exists an integer k such that n = 2k. • An is odd if there exists an integer k such that n = 2k+1. • Note: An integer is either even or odd, but not both. • This is an immediate consequence of the division algorithm: If a and b are positive integers, then there exist u ...
Document
... Conjunction is a binary operator in that it operates on two propositions when creating compound proposition. On the other hand, negation is a unary operator (the only non-trivial one possible). ...
... Conjunction is a binary operator in that it operates on two propositions when creating compound proposition. On the other hand, negation is a unary operator (the only non-trivial one possible). ...
First-Order Loop Formulas for Normal Logic Programs
... variables, we can hopefully avoid this problem of having to compute similar loops and loop formulas every time a program is grounded on a domain. Thus extending loop formulas in logic programming to first-order case is not only theoretically interesting, but may also be of practical relevance. Speci ...
... variables, we can hopefully avoid this problem of having to compute similar loops and loop formulas every time a program is grounded on a domain. Thus extending loop formulas in logic programming to first-order case is not only theoretically interesting, but may also be of practical relevance. Speci ...
The Bang-Bang Funnel Controller (long version)
... to problems concerning the existence of solutions; however, by implementing the switching logic with some hysteresis effect this solvability problem can be avoided. For switched systems (average) dwell times are important, because in practical applications arbitrarily fast switching is often not pos ...
... to problems concerning the existence of solutions; however, by implementing the switching logic with some hysteresis effect this solvability problem can be avoided. For switched systems (average) dwell times are important, because in practical applications arbitrarily fast switching is often not pos ...
Comments on the 2nd order bootstrap relation
... to solve it was incorrect. In this note we demonstrate that these objections are totally unfounded. They are a result of a misinterpretation of the potential used in [2], which is a different quantity as compared to the kernel used in [1,3]. We also derive the 2nd order bootstrap relation of [1] in ...
... to solve it was incorrect. In this note we demonstrate that these objections are totally unfounded. They are a result of a misinterpretation of the potential used in [2], which is a different quantity as compared to the kernel used in [1,3]. We also derive the 2nd order bootstrap relation of [1] in ...
Field Theory and Standard Model
... mass terms. The first two terms, mass terms for up-type- and down-type-quarks, respectively, cannot be diagonalised simultaneously, and this misalignment leads to the CKM matrix and flavour physics [6]. Similarly, the last two terms give rise to lepton masses and neutrino mixings [7]. ...
... mass terms. The first two terms, mass terms for up-type- and down-type-quarks, respectively, cannot be diagonalised simultaneously, and this misalignment leads to the CKM matrix and flavour physics [6]. Similarly, the last two terms give rise to lepton masses and neutrino mixings [7]. ...
Recurrent points and hyperarithmetic sets
... 1·3 REMARK The above use of AC could be reduced to an application of DC by working in L[a, f ] and appealing to Shoenfield’s absoluteness theorem. We may use the following lemma since in a metric space second countability and separability are equivalent conditions. 1·4 LEMMA (AC) In a second countab ...
... 1·3 REMARK The above use of AC could be reduced to an application of DC by working in L[a, f ] and appealing to Shoenfield’s absoluteness theorem. We may use the following lemma since in a metric space second countability and separability are equivalent conditions. 1·4 LEMMA (AC) In a second countab ...
