Thesis Proposal: A Logical Foundation for Session-based
... In Section 3 I develop the interpretation of linear logic as session types that serves as the basis for my work. It has a few variations from that of [5] in that it does not commit to the π-calculus a priori, developing a proof term assignment that can be used as a language for session-typed communi ...
... In Section 3 I develop the interpretation of linear logic as session types that serves as the basis for my work. It has a few variations from that of [5] in that it does not commit to the π-calculus a priori, developing a proof term assignment that can be used as a language for session-typed communi ...
Carnap and Quine on the analytic-synthetic - Philsci
... used in favour of these frameworks. These pragmatic arguments for choosing particular linguistic frameworks have immediate repercussions for the analyticity of the non-factual statements in these frameworks. It will transpire that the class of statements Quine would accept as analytic is much more ...
... used in favour of these frameworks. These pragmatic arguments for choosing particular linguistic frameworks have immediate repercussions for the analyticity of the non-factual statements in these frameworks. It will transpire that the class of statements Quine would accept as analytic is much more ...
Gödel`s correspondence on proof theory and constructive mathematics
... error in the proof of a lemma ((3.3) in [Herbrand, 1930]) to Herbrand’s fundamental theorem (“Herbrand’s Theorem”) in his thesis. Gödel seems to have noticed it in the early 1940s and to have found a satisfactory correction of the lemma. However, he did not announce his discovery and there was no g ...
... error in the proof of a lemma ((3.3) in [Herbrand, 1930]) to Herbrand’s fundamental theorem (“Herbrand’s Theorem”) in his thesis. Gödel seems to have noticed it in the early 1940s and to have found a satisfactory correction of the lemma. However, he did not announce his discovery and there was no g ...
Inference and Proofs - Dartmouth Math Home
... Now m2 must have an even number of prime factors (counting each prime factor as many times as it occurs) as must n2 . But 5n2 has an odd number of prime factors. Thus a product of an even number of prime factors is equal to a product of an odd number of prime factors, which is a contradiction since ...
... Now m2 must have an even number of prime factors (counting each prime factor as many times as it occurs) as must n2 . But 5n2 has an odd number of prime factors. Thus a product of an even number of prime factors is equal to a product of an odd number of prime factors, which is a contradiction since ...
Logic and Sets
... So 12 falls into a third category — numbers which are less than the sum of their proper factors. Such numbers are said to be abundant. Next, for 18, its proper factors are 1, 2, 3, 6, and 9, and 1 + 2 + 3 + 6 + 9 = 21 > 18. Hence, 18 is abundant. Similarly, 20 and 24 are abundant. Next comes 28. Its ...
... So 12 falls into a third category — numbers which are less than the sum of their proper factors. Such numbers are said to be abundant. Next, for 18, its proper factors are 1, 2, 3, 6, and 9, and 1 + 2 + 3 + 6 + 9 = 21 > 18. Hence, 18 is abundant. Similarly, 20 and 24 are abundant. Next comes 28. Its ...
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
... And, or, not, if . . . then (or implies) are called (sentential) connectives. Using them we can define more connectives, for example 2 is prime iff 2 is odd can be defined as (If 2 is prime then 2 is odd) and (if 2 is odd then 2 is prime). The truth value of any compound sentence is determined compl ...
... And, or, not, if . . . then (or implies) are called (sentential) connectives. Using them we can define more connectives, for example 2 is prime iff 2 is odd can be defined as (If 2 is prime then 2 is odd) and (if 2 is odd then 2 is prime). The truth value of any compound sentence is determined compl ...
An argumentation framework in default logic
... themselves in cases in which the definitions boil down to directly applying this criterion to the subtheories of the premises. For this reason I will confine myself to discussing such cases. Consider first an example in which this method gives satisfactory results. Assume that the inconsistent set { ...
... themselves in cases in which the definitions boil down to directly applying this criterion to the subtheories of the premises. For this reason I will confine myself to discussing such cases. Consider first an example in which this method gives satisfactory results. Assume that the inconsistent set { ...
Horn Belief Contraction: Remainders, Envelopes and Complexity
... It is assumed that there is a fixed finite set of propositional variables. We use 0 and 1 for representing truth values. The set of truth assignments satisfying (resp., falsifying) a propositional formula ψ is denoted by T (ψ) (resp., F (ψ)). For formulas ψ, ϕ it holds that ψ |= ϕ (i.e., ϕ is a cons ...
... It is assumed that there is a fixed finite set of propositional variables. We use 0 and 1 for representing truth values. The set of truth assignments satisfying (resp., falsifying) a propositional formula ψ is denoted by T (ψ) (resp., F (ψ)). For formulas ψ, ϕ it holds that ψ |= ϕ (i.e., ϕ is a cons ...
Logic and Discrete Mathematics for Computer Scientists
... rigorous but informal proofs to be presented. The formal approach to the presentation of material has, we believe, a number of significant advantages, especially for Computer Science students, but also, for more traditional math students who might find their way into the course. In mathematics depar ...
... rigorous but informal proofs to be presented. The formal approach to the presentation of material has, we believe, a number of significant advantages, especially for Computer Science students, but also, for more traditional math students who might find their way into the course. In mathematics depar ...
CS389L: Automated Logical Reasoning Lecture 1
... Formulas F1 and F2 are equivalent (written F1 ⇔ F2 ) iff for all interpretations I , I |= F1 ↔ F2 F1 ⇔ F2 iff F1 ↔ F2 is valid ...
... Formulas F1 and F2 are equivalent (written F1 ⇔ F2 ) iff for all interpretations I , I |= F1 ↔ F2 F1 ⇔ F2 iff F1 ↔ F2 is valid ...
Symbolic Logic I: The Propositional Calculus
... Therefore, tv(P ∨ Q) = 1 whenever at least one of tv(P ) = 1 or tv(Q) = 1; tv(P ∨ Q) = 0 otherwise, i.e., when both tv(P ) = 0 and tv(Q) = 0. 2.5. Implication. The truth-values produced by the operations of identity, negation, conjunction and disjunction are intuitively straightforward, but the trut ...
... Therefore, tv(P ∨ Q) = 1 whenever at least one of tv(P ) = 1 or tv(Q) = 1; tv(P ∨ Q) = 0 otherwise, i.e., when both tv(P ) = 0 and tv(Q) = 0. 2.5. Implication. The truth-values produced by the operations of identity, negation, conjunction and disjunction are intuitively straightforward, but the trut ...
A Pebble Weighted Automata and Weighted Logics
... More precisely, we introduce pebble weighted automata on words and establish expressive equivalence to weighted first-order logic with a quantitative extension of the Boolean transitive closure, extending the classical Boolean case for words [Engelfriet and Hoogeboom 2007]. Our equivalence proof mak ...
... More precisely, we introduce pebble weighted automata on words and establish expressive equivalence to weighted first-order logic with a quantitative extension of the Boolean transitive closure, extending the classical Boolean case for words [Engelfriet and Hoogeboom 2007]. Our equivalence proof mak ...
Dealing with imperfect information in Strategy Logic
... Concerning ATL, many variants have been introduced that deal with imperfect information [12, 14, 22, 13]. Some of these numerous logics deal with strategizing under imperfect information, some with reasoning about knowledge; because it is not natural to reason about the knowledge of agents with impe ...
... Concerning ATL, many variants have been introduced that deal with imperfect information [12, 14, 22, 13]. Some of these numerous logics deal with strategizing under imperfect information, some with reasoning about knowledge; because it is not natural to reason about the knowledge of agents with impe ...
Multiverse Set Theory and Absolutely Undecidable Propositions
... o↵ered itself that there are absolutely undecidable propositions in mathematics, propositions that cannot be solved at all, by any means. If that were the case, one could throw doubt on the idea that mathematical propositions have a determined truth-value and that there is a unique well-determined r ...
... o↵ered itself that there are absolutely undecidable propositions in mathematics, propositions that cannot be solved at all, by any means. If that were the case, one could throw doubt on the idea that mathematical propositions have a determined truth-value and that there is a unique well-determined r ...
Group knowledge is not always distributed (neither is it always implicit)
... Interestingly, we are able to prove a property like that in Lemma 3.1 even when the G operator is involved. Theorem 3.3. Let X and Y range over hK1 ,K2 , . . . ,Km ,Gj. Then: £Xw ⇔ £Yw. Theorem 3.3 has, for both the reading as group knowledge as well as that of a receiving agent for G, some remarkab ...
... Interestingly, we are able to prove a property like that in Lemma 3.1 even when the G operator is involved. Theorem 3.3. Let X and Y range over hK1 ,K2 , . . . ,Km ,Gj. Then: £Xw ⇔ £Yw. Theorem 3.3 has, for both the reading as group knowledge as well as that of a receiving agent for G, some remarkab ...
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 ...
Constraint Logic Programming with Hereditary Harrop Formula
... Herbrand universe by providing the ability to program with Horn clauses over different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et a ...
... Herbrand universe by providing the ability to program with Horn clauses over different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et a ...
Characterizations of stable model semantics for logic programs with
... dynamic CSPs), which are useful in modeling configuration and design problems. When the head of a rule is allowed to be a disjunction of constraint atoms, logic programs become capable of expressing, not only conditional constraints, but also disjunctive constraints, both of which have been investiga ...
... dynamic CSPs), which are useful in modeling configuration and design problems. When the head of a rule is allowed to be a disjunction of constraint atoms, logic programs become capable of expressing, not only conditional constraints, but also disjunctive constraints, both of which have been investiga ...
Introduction to Modal and Temporal Logic
... l = 0: So Γ ⊢ ψ because ψ ∈ Γ. But M Γ implies M ψ for all ψ ∈ Γ. l = 0: So Γ ⊢ ψ because ψ is an axiom schema instance. By Eg 1, Ex 1, Ex 2, Eg 2, we know ∅ |= ψ for every axiom schema instance ψ, hence Γ |= ψ. Ind. Hyp. : Theorem holds for all derivations of length less than some k > 0. Ind. S ...
... l = 0: So Γ ⊢ ψ because ψ ∈ Γ. But M Γ implies M ψ for all ψ ∈ Γ. l = 0: So Γ ⊢ ψ because ψ is an axiom schema instance. By Eg 1, Ex 1, Ex 2, Eg 2, we know ∅ |= ψ for every axiom schema instance ψ, hence Γ |= ψ. Ind. Hyp. : Theorem holds for all derivations of length less than some k > 0. Ind. S ...
Effectively Polynomial Simulations
... mulas. More generally for any class of formulas, and We first recall the usual notion of polynomial simula- any two proof systems that can prove formulas of this tions given in the literature. In what follows, we will be type, we can define a p-simulation with respect to this working with boolean fo ...
... mulas. More generally for any class of formulas, and We first recall the usual notion of polynomial simula- any two proof systems that can prove formulas of this tions given in the literature. In what follows, we will be type, we can define a p-simulation with respect to this working with boolean fo ...
Document
... of three usual operators: the negation operator ¬ (unary), the conjunction operator ∧ (binary) and the disjunction operator ∨ (binary), each of them being used to connect formulae (the variables themselves are atomic formulae). Insofar as a propositional formula is built in an inductive way (since t ...
... of three usual operators: the negation operator ¬ (unary), the conjunction operator ∧ (binary) and the disjunction operator ∨ (binary), each of them being used to connect formulae (the variables themselves are atomic formulae). Insofar as a propositional formula is built in an inductive way (since t ...