Interpreting and Applying Proof Theories for Modal Logic
... These syntactic items allow us to construct more general kinds of sequents. ...
... These syntactic items allow us to construct more general kinds of sequents. ...
PowerPoint file for CSL 02, Edinburgh, UK
... semi-classical principles are conjectured not to be derivable in HA. If the scheme S0n–DNE is not derivable from the scheme P0n–LEM, then the conjecture is proved for the n-level. The conjecture have been solved for n=1, 2 levels, which include all of the LCM semiclassical principles. It is still op ...
... semi-classical principles are conjectured not to be derivable in HA. If the scheme S0n–DNE is not derivable from the scheme P0n–LEM, then the conjecture is proved for the n-level. The conjecture have been solved for n=1, 2 levels, which include all of the LCM semiclassical principles. It is still op ...
Finite Model Theory
... accepts an input 1K n , if there is a computation I1 ,K, Ik so that I1 = q1 1K n and Ik is accepting. The time of the computation I1 ,K, Ik is k, so that each instruction is thought to take one unit of time. The space of I1 ,K, Ik is the maximum length of Ii . Note, that the space of a computation i ...
... accepts an input 1K n , if there is a computation I1 ,K, Ik so that I1 = q1 1K n and Ik is accepting. The time of the computation I1 ,K, Ik is k, so that each instruction is thought to take one unit of time. The space of I1 ,K, Ik is the maximum length of Ii . Note, that the space of a computation i ...
Constructive Mathematics in Theory and Programming Practice
... • His results and proofs were formally consistent with Brouwer's intuitionistic mathematics (INT), recursive constructive mathematics (RUSS), and classical (that is, traditional) mathematics (CLASS): every theorem proved in Bishop is also a theorem, with the same proof, in INT, RUSS, and CLASS. Alth ...
... • His results and proofs were formally consistent with Brouwer's intuitionistic mathematics (INT), recursive constructive mathematics (RUSS), and classical (that is, traditional) mathematics (CLASS): every theorem proved in Bishop is also a theorem, with the same proof, in INT, RUSS, and CLASS. Alth ...
Lecture_Notes (original)
... We can argue that the P_(n+1) = P_n + n+1. Every new cut intersects each of the old cuts in one unique place. Hence each new cut creates 1 more region than the number of cuts already made, because it creates a region as it exits the circle. This is called a recurrence equation and we can solve it di ...
... We can argue that the P_(n+1) = P_n + n+1. Every new cut intersects each of the old cuts in one unique place. Hence each new cut creates 1 more region than the number of cuts already made, because it creates a region as it exits the circle. This is called a recurrence equation and we can solve it di ...
Game Theory: Logic, Set and Summation Notation
... A “tautology” is a compound statement that is always true (like p ∨[q ⇒ ¬p], for example). A “theorem” (or proposition, or lemma or corollary) is a tautology of the form [p1 ∧ p2 ∧ . . . ∧ pk ] ⇒ q. The statements p1 , p2 , . . . , pk are “assumptions.” We would generally write something like: “Assu ...
... A “tautology” is a compound statement that is always true (like p ∨[q ⇒ ¬p], for example). A “theorem” (or proposition, or lemma or corollary) is a tautology of the form [p1 ∧ p2 ∧ . . . ∧ pk ] ⇒ q. The statements p1 , p2 , . . . , pk are “assumptions.” We would generally write something like: “Assu ...
Solutions to Workbook Exercises Unit 16: Categorical Propositions
... Symbolize the following opinions about politicians using the symbolization key provided. For each of the propositions, write down the canonical reading: U.D.: politicians ...
... Symbolize the following opinions about politicians using the symbolization key provided. For each of the propositions, write down the canonical reading: U.D.: politicians ...
Welcome to CS 39 - Dartmouth Computer Science
... Proof by induction To prove a theorem by induction: • Prove the theorem for a general case by assuming the same theorem to be true (“induction hypothesis”) for all smaller cases. • Separately prove the theorem, without making any assumptions, for all “base” cases, i.e., those cases for which there i ...
... Proof by induction To prove a theorem by induction: • Prove the theorem for a general case by assuming the same theorem to be true (“induction hypothesis”) for all smaller cases. • Separately prove the theorem, without making any assumptions, for all “base” cases, i.e., those cases for which there i ...
PDF
... section. In this view, a receiver may expect to receive a term {t}k according to the protocol, but unless she also has k −1 , she cannot get t (using only this encrypted term). is is a form of database knowledge: an agent A has only that information explicitly stored in the agent’s database. However ...
... section. In this view, a receiver may expect to receive a term {t}k according to the protocol, but unless she also has k −1 , she cannot get t (using only this encrypted term). is is a form of database knowledge: an agent A has only that information explicitly stored in the agent’s database. However ...
CSE 20 - Lecture 14: Logic and Proof Techniques
... university in USA where every department has at least 20 faculty and at least one noble laureate.” There is an university in USA where every department has less than 20 faculty and at least one noble laureate. All universitis in USA where every department has at least 20 faculty and at least one nob ...
... university in USA where every department has at least 20 faculty and at least one noble laureate.” There is an university in USA where every department has less than 20 faculty and at least one noble laureate. All universitis in USA where every department has at least 20 faculty and at least one nob ...
Document
... the proposition "3+2=6" if false, but the proposition "¬(3 + 2 = 6)" is true. "¬(3 + 2 = 6)" is not the same as "3 + 2 = 5". the effect of "¬" is shown in the Truth Table: p ...
... the proposition "3+2=6" if false, but the proposition "¬(3 + 2 = 6)" is true. "¬(3 + 2 = 6)" is not the same as "3 + 2 = 5". the effect of "¬" is shown in the Truth Table: p ...
Discordance Detection in Regional Ordinance: Ontology
... 2.1 Discordance The logical inconsistency becomes apparent only when appear in a set of propositions. Howboth of and ever, the inconsistency may not be seen from the superficial sentences of the legal code. To clarify such latent inconsistency, we need to supply some premises of the rules ( ). The ...
... 2.1 Discordance The logical inconsistency becomes apparent only when appear in a set of propositions. Howboth of and ever, the inconsistency may not be seen from the superficial sentences of the legal code. To clarify such latent inconsistency, we need to supply some premises of the rules ( ). The ...
Document
... An argument in propositional logic is a sequence of propositions. All but the final proposition in the argument are called premises and the final proposition is called the conclusion. An argument is valid if the truth of all its premises implies that the conclusion is true. ...
... An argument in propositional logic is a sequence of propositions. All but the final proposition in the argument are called premises and the final proposition is called the conclusion. An argument is valid if the truth of all its premises implies that the conclusion is true. ...
And this is just one theorem prover!
... Over the next three decades • Many large theorem proving systems are born ...
... Over the next three decades • Many large theorem proving systems are born ...
(A B) |– A
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
Clausal Logic and Logic Programming in Algebraic Domains*
... In this paper we show how to represent the Smyth powerdomain of a coherent algebraic dcpo using an elementary logic built over such a domain. This is a clausal logic, different from the modal logic introduced by Winskel [Win83] for the Smyth powerdomain. We obtain the logic by regarding finite sets ...
... In this paper we show how to represent the Smyth powerdomain of a coherent algebraic dcpo using an elementary logic built over such a domain. This is a clausal logic, different from the modal logic introduced by Winskel [Win83] for the Smyth powerdomain. We obtain the logic by regarding finite sets ...
Notions of locality and their logical characterizations over nite
... for proving expressibility bounds for rst-order logic. A number of results proving expressibility bounds explain the nature of the limitations of rst-order logic by saying that it can only express local properties. Intuitively, one cannot grasp the whole structure; instead, to answer a rst-order ...
... for proving expressibility bounds for rst-order logic. A number of results proving expressibility bounds explain the nature of the limitations of rst-order logic by saying that it can only express local properties. Intuitively, one cannot grasp the whole structure; instead, to answer a rst-order ...
Uninformed Search
... more existing sentences S. S is called the premise and X the conclusion of the rule. • Proof procedure: a set of inference rules and a procedure of how to use these rules • If X can be generated from S by proof procedure i, we say X is derived from S by i, denoted S |i X, or S | X. • Soundness. An i ...
... more existing sentences S. S is called the premise and X the conclusion of the rule. • Proof procedure: a set of inference rules and a procedure of how to use these rules • If X can be generated from S by proof procedure i, we say X is derived from S by i, denoted S |i X, or S | X. • Soundness. An i ...
brouwer`s intuitionism as a self-interpreted mathematical theory
... Brouwer’s intuitionistic analysis (BIA): it is the mathematical development of the concept of the intuitionistic continuum, which is described as an appropriate spread, based on a corpus of intuitionistic principles and concepts. Brouwer never used axioms in BIA and he tried to justify all his princ ...
... Brouwer’s intuitionistic analysis (BIA): it is the mathematical development of the concept of the intuitionistic continuum, which is described as an appropriate spread, based on a corpus of intuitionistic principles and concepts. Brouwer never used axioms in BIA and he tried to justify all his princ ...
Classical Propositional Logic
... DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refined versions are still the ...
... DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refined versions are still the ...
(A B) |– A
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
... 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend the set o ...
A modal perspective on monadic second
... As a by-product of our investigations we obtain a simple, effective procedure (inspired by the approach of ten Cate [8]) that translates MSOsentences to equivalent formulae of Second-Order Propositional Modal Logic with Universal Modality (SOPML(E )). This implies that the expressive power of SOPML( ...
... As a by-product of our investigations we obtain a simple, effective procedure (inspired by the approach of ten Cate [8]) that translates MSOsentences to equivalent formulae of Second-Order Propositional Modal Logic with Universal Modality (SOPML(E )). This implies that the expressive power of SOPML( ...