LINEAR LOGIC AS A FRAMEWORK FOR SPECIFYING SEQUENT
... can specify a variety of proof systems for object-level systems. By making use of classical linear logic, we are able to capture not only natural deduction proof systems but also many sequent calculus proof systems. We will present our scheme for encoding proof systems in linear logic and show sever ...
... can specify a variety of proof systems for object-level systems. By making use of classical linear logic, we are able to capture not only natural deduction proof systems but also many sequent calculus proof systems. We will present our scheme for encoding proof systems in linear logic and show sever ...
A Note on the Relation between Inflationary Fixpoints and Least
... from sets of vertices to sets of vertices but more general fixpoint constructs are allowed that least fixpoints over monotone functions, and “higher-order” fixpoint logics, where we retain monotone fixpoint inductions but allow fixpoints of operators over a function space. An example for the first a ...
... from sets of vertices to sets of vertices but more general fixpoint constructs are allowed that least fixpoints over monotone functions, and “higher-order” fixpoint logics, where we retain monotone fixpoint inductions but allow fixpoints of operators over a function space. An example for the first a ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... from Stockholm University in 1957 under the supervision of Anders Wedberg. Kanger’s dissertation, Provability in Logic, was remarkably short, only 47 pages, but also very rich in new ideas and results. By combining Gentzen-style techniques with a model theory à la Tarski, Kanger obtained new and sim ...
... from Stockholm University in 1957 under the supervision of Anders Wedberg. Kanger’s dissertation, Provability in Logic, was remarkably short, only 47 pages, but also very rich in new ideas and results. By combining Gentzen-style techniques with a model theory à la Tarski, Kanger obtained new and sim ...
Note 2 - inst.eecs.berkeley.edu
... So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the fact that using finite means, we can guarantee the truth of a statement with infinitely many cases. More specifica ...
... So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the fact that using finite means, we can guarantee the truth of a statement with infinitely many cases. More specifica ...
Note 2 - EECS: www-inst.eecs.berkeley.edu
... So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the fact that using finite means, we can guarantee the truth of a statement with infinitely many cases. More specifica ...
... So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the fact that using finite means, we can guarantee the truth of a statement with infinitely many cases. More specifica ...
Insights into Modal Slash Logic and Modal Decidability
... player E selects j ∈ {0, 1} and the play continues with the position (~a,~ij, χj ). It is the player A who chooses if ψ = (χ0 ∧ χ1 ). If, again, ψ = (∃x/W )χ, player E selects b ∈ M and the play continues with the position (~ab,~i, χ); note that the rule in no way utilizes the independence indicatio ...
... player E selects j ∈ {0, 1} and the play continues with the position (~a,~ij, χj ). It is the player A who chooses if ψ = (χ0 ∧ χ1 ). If, again, ψ = (∃x/W )χ, player E selects b ∈ M and the play continues with the position (~ab,~i, χ); note that the rule in no way utilizes the independence indicatio ...
A proposition is any declarative sentence (including mathematical
... Definition: A tautology, or a law of propositional logic, is a statement which is always true A contradiction is a statement whose truth function has all Fs as outputs (in other words, it’s a statement whose negation is a tautology). Two statements are called propositionally equivalent if a tautolog ...
... Definition: A tautology, or a law of propositional logic, is a statement which is always true A contradiction is a statement whose truth function has all Fs as outputs (in other words, it’s a statement whose negation is a tautology). Two statements are called propositionally equivalent if a tautolog ...
Almost-certain eventualities and abstract probabilities in quantitative
... almost certainly: no matter where the system is started, the state s will evenually be H, and will eventually be T , provided 0 < p < 1. An abstract probability is one which — like p above — is known only to be neither 0 nor 1: beyond that, its precise value is immaterial for the conclusions that ar ...
... almost certainly: no matter where the system is started, the state s will evenually be H, and will eventually be T , provided 0 < p < 1. An abstract probability is one which — like p above — is known only to be neither 0 nor 1: beyond that, its precise value is immaterial for the conclusions that ar ...
On Dummett`s Pragmatist Justification Procedure
... According to Dummett [1, 2], the analysis of the deductive meaning of a logical constant into introduction and elimination rules accounts for two ...
... According to Dummett [1, 2], the analysis of the deductive meaning of a logical constant into introduction and elimination rules accounts for two ...
Inference and Proofs - Dartmouth Math Home
... We concluded our last section with a proof that the sum of two even numbers is even. That proof contained several crucial ingredients. First, we introduced symbols for members of the universe of integers. In other words, rather than saying “suppose we have two integers,” we introduced symbols for th ...
... We concluded our last section with a proof that the sum of two even numbers is even. That proof contained several crucial ingredients. First, we introduced symbols for members of the universe of integers. In other words, rather than saying “suppose we have two integers,” we introduced symbols for th ...
First-order possibility models and finitary
... A propositional modal logic has a finitary completeness proof if it has a canonical model all of whose possibilities are finitely specified in this sense. This was one of Humberstone’s original motivations for considering possibility models. For many normal modal logics extending K with standard axi ...
... A propositional modal logic has a finitary completeness proof if it has a canonical model all of whose possibilities are finitely specified in this sense. This was one of Humberstone’s original motivations for considering possibility models. For many normal modal logics extending K with standard axi ...
In order to define the notion of proof rigorously, we would have to
... P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true because if both P and P ⇒⊥ were true then we could conclude ...
... P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true because if both P and P ⇒⊥ were true then we could conclude ...
Chapter X: Computational Complexity of Propositional Fuzzy Logics
... more difficult than tautologousness. This chapter tries to answer this question by showing coNP-containment (hence, coNP-completeness) for the universal fragment of the theory of these algebras. Thus we are able to avail ourselves of the classical dichotomy after all, albeit on a metamathematical le ...
... more difficult than tautologousness. This chapter tries to answer this question by showing coNP-containment (hence, coNP-completeness) for the universal fragment of the theory of these algebras. Thus we are able to avail ourselves of the classical dichotomy after all, albeit on a metamathematical le ...
Strong Completeness and Limited Canonicity for PDL
... is true in a world (i.e. a maximal consistent set) of the canonical model iff it is an element of that world. In other words: at the formula level, there is agreement between the semantics and the proof theoretical aspects of the canonical model. Therefore we call this property formula harmony, and ...
... is true in a world (i.e. a maximal consistent set) of the canonical model iff it is an element of that world. In other words: at the formula level, there is agreement between the semantics and the proof theoretical aspects of the canonical model. Therefore we call this property formula harmony, and ...
The Logic of Atomic Sentences
... This is a step-by-step demonstration that the conclusion of Argument 3 must be true if the 3 premises of Argument 3 are true Each step consists of a simple, obvious, valid inference William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
... This is a step-by-step demonstration that the conclusion of Argument 3 must be true if the 3 premises of Argument 3 are true Each step consists of a simple, obvious, valid inference William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
Default reasoning using classical logic
... and 5 we discuss how the models presented in Section 3 can be treated as classical models of propositional logic. We present algorithms that associate for each nite default theory a classical propositional theory that characterizes its extensions. Then, in Section 6 we use constraint satisfaction t ...
... and 5 we discuss how the models presented in Section 3 can be treated as classical models of propositional logic. We present algorithms that associate for each nite default theory a classical propositional theory that characterizes its extensions. Then, in Section 6 we use constraint satisfaction t ...
Chapter 5 - Stanford Lagunita
... idempotence if the need arises in a proof. Thus a chain of equivalences of the sort we gave on page 120 is a legitimate component of an informal proof. Of course, if you are asked to prove one of the named equivalences, say one of the distribution or DeMorgan laws, then you shouldn’t presuppose it i ...
... idempotence if the need arises in a proof. Thus a chain of equivalences of the sort we gave on page 120 is a legitimate component of an informal proof. Of course, if you are asked to prove one of the named equivalences, say one of the distribution or DeMorgan laws, then you shouldn’t presuppose it i ...
Conjunctive normal form - Computer Science and Engineering
... functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to tell whether a propositional expre ...
... functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to tell whether a propositional expre ...
Decision procedures in Algebra and Logic
... in the sense of algebraic geometry). Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant universe. Identities contain no connectives, existentially quantified variables, or relations of any kind o ...
... in the sense of algebraic geometry). Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant universe. Identities contain no connectives, existentially quantified variables, or relations of any kind o ...
brouwer`s intuitionism as a self-interpreted mathematical theory
... in BIA and he tried to justify all his principles on conceptual grounds. All the above theories are constructive, i.e., they contain, tacitly or not, some constructive principles which guide the execution of proofs and the formation of concepts. In that way, the truth of the fundamental intuitions o ...
... in BIA and he tried to justify all his principles on conceptual grounds. All the above theories are constructive, i.e., they contain, tacitly or not, some constructive principles which guide the execution of proofs and the formation of concepts. In that way, the truth of the fundamental intuitions o ...
In terlea v ed
... are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes an atomic transition, the others are inactive. Thus, rather than input/output pairs, execution sequences of the atomic instructions of sequential process ...
... are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes an atomic transition, the others are inactive. Thus, rather than input/output pairs, execution sequences of the atomic instructions of sequential process ...
Proofs in Propositional Logic
... How to declare propositional variables A propositional variable is just a variable of type Prop. So, you may just use the Parameter command for declaring a new propositional variable : ...
... How to declare propositional variables A propositional variable is just a variable of type Prop. So, you may just use the Parameter command for declaring a new propositional variable : ...
Proofs in Propositional Logic
... How to declare propositional variables A propositional variable is just a variable of type Prop. So, you may just use the Parameter command for declaring a new propositional variable : ...
... How to declare propositional variables A propositional variable is just a variable of type Prop. So, you may just use the Parameter command for declaring a new propositional variable : ...
The Development of Mathematical Logic from Russell to Tarski
... Hilbert’s famous Foundations of Geometry ( 1899). In his presentation to the International Congress of Philosophy in 1900, Pieri emphasized that the study of geometry is following arithmetic in becoming more and more “the study of a certain order of logical relations; in freeing itself little by lit ...
... Hilbert’s famous Foundations of Geometry ( 1899). In his presentation to the International Congress of Philosophy in 1900, Pieri emphasized that the study of geometry is following arithmetic in becoming more and more “the study of a certain order of logical relations; in freeing itself little by lit ...
The Development of Categorical Logic
... to establish various independence results. In Fourman (1980) , it was shown how the construction of the usual cumulative hierarchy of sets generated by a collection of atoms can be carried out within a locally small complete topos E (in particular, any Grothendieck topos). This leads to a topos E*—i ...
... to establish various independence results. In Fourman (1980) , it was shown how the construction of the usual cumulative hierarchy of sets generated by a collection of atoms can be carried out within a locally small complete topos E (in particular, any Grothendieck topos). This leads to a topos E*—i ...
Jesús Mosterín
Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.