THE MODEL CHECKING PROBLEM FOR INTUITIONISTIC
... whether a given formula is satisfied by a given intuitionistic Kripke model—for IPC is P-complete [16], even for the fragment with two variables only [17]. More surprisingly, for the fragment with one variable IPC1 we show the model checking problem to be AC1 -complete. To our knowledge, this is the ...
... whether a given formula is satisfied by a given intuitionistic Kripke model—for IPC is P-complete [16], even for the fragment with two variables only [17]. More surprisingly, for the fragment with one variable IPC1 we show the model checking problem to be AC1 -complete. To our knowledge, this is the ...
PPT
... A proof of Q from H1, H2, … Hk is finite sequence of propositional forms Q 1, Q 2, … Qn such that Qn is same as Q and every Qj is either one of Hi, (i = 1, 2, … , k) or it follows from the proceedings by the logic rules. Note: In these proofs we will follow the following formats: We begin with by li ...
... A proof of Q from H1, H2, … Hk is finite sequence of propositional forms Q 1, Q 2, … Qn such that Qn is same as Q and every Qj is either one of Hi, (i = 1, 2, … , k) or it follows from the proceedings by the logic rules. Note: In these proofs we will follow the following formats: We begin with by li ...
Morley`s number of countable models
... both ϕ and ¬ϕ would be satisfied by all sequences. Suppose t satisfies C1 for formulas containing n free variables. t then satisfies C1 for formulas containing n + 1 free variables, since otherwise both ϕ and ¬ϕ would be satisfied by the objects ha0 , . . . , an , . . . i.2 The proof that t satisfie ...
... both ϕ and ¬ϕ would be satisfied by all sequences. Suppose t satisfies C1 for formulas containing n free variables. t then satisfies C1 for formulas containing n + 1 free variables, since otherwise both ϕ and ¬ϕ would be satisfied by the objects ha0 , . . . , an , . . . i.2 The proof that t satisfie ...
A pragmatic dialogic interpretation of bi
... 1 Introduction. A mathematical prelude. The mathematical case study of this paper is a variant of Cecylia Rauzer’s bi-intuitionistic logic [48, 49] (called Heyting-Brouwer logic by Rauszer) and the relations between the two parts that can be identified within it, namely intuitionistic logic, on one ...
... 1 Introduction. A mathematical prelude. The mathematical case study of this paper is a variant of Cecylia Rauzer’s bi-intuitionistic logic [48, 49] (called Heyting-Brouwer logic by Rauszer) and the relations between the two parts that can be identified within it, namely intuitionistic logic, on one ...
gödel`s completeness theorem with natural language formulas
... We give a formalization of the mathematical language used in the 2example. We shall work with natural language constructs like “for all x” instead of introducing formal quantifiers “∀x”. In this way the meaning or the semantics of formulas becomes self-explanatory. For the purposes of this paper we ...
... We give a formalization of the mathematical language used in the 2example. We shall work with natural language constructs like “for all x” instead of introducing formal quantifiers “∀x”. In this way the meaning or the semantics of formulas becomes self-explanatory. For the purposes of this paper we ...
Complete Sequent Calculi for Induction and Infinite Descent
... The eliminability of cut in LKID implies the consistency of Peano arithmetic. Hence there is no elementary proof of cut-eliminability in LKID. ...
... The eliminability of cut in LKID implies the consistency of Peano arithmetic. Hence there is no elementary proof of cut-eliminability in LKID. ...
Herbrands Theorem
... - Every interpretation I of S contains an interpretation I’ of S’ - So, if I’ falsifies S’, then I must also falsify S’ - Since S’ is falsified by every interpretation I’, it must also be falsified by every interpretation I of S - i.e. S is falsified by every interpretation of S - Hence S is unsatis ...
... - Every interpretation I of S contains an interpretation I’ of S’ - So, if I’ falsifies S’, then I must also falsify S’ - Since S’ is falsified by every interpretation I’, it must also be falsified by every interpretation I of S - i.e. S is falsified by every interpretation of S - Hence S is unsatis ...
math 55: homework #2 solutions - Harvard Mathematics Department
... we check that the predicate is true in the case that the antecedent is true. If x and y are distinct elements of the domain, as indicated by the antecedent, then one must be a and the other b . Then, any third choice of element z of the domain must also either be equal to a or b , and hence to one o ...
... we check that the predicate is true in the case that the antecedent is true. If x and y are distinct elements of the domain, as indicated by the antecedent, then one must be a and the other b . Then, any third choice of element z of the domain must also either be equal to a or b , and hence to one o ...
Scharp on Replacing Truth
... by other problematic instances of T (instances involving the Curry sentence, liar pairs, Yablo’s paradox, and so on), but not shared with the unproblematic instances of T (instances such as ‘snow is white’, ‘1+1 = 5’ and so on). Extant examples of this strategy include the claim that the bad instanc ...
... by other problematic instances of T (instances involving the Curry sentence, liar pairs, Yablo’s paradox, and so on), but not shared with the unproblematic instances of T (instances such as ‘snow is white’, ‘1+1 = 5’ and so on). Extant examples of this strategy include the claim that the bad instanc ...
Advanced Topics in Theoretical Computer Science
... Decidability and Undecidability results Theorem. It is undecidable whether a first order logic formula is valid. Proof. Suppose there is an algorithm P that, given a first order logic and a formula in that logic, decides whether that formula is valid. We use P to give a decision algorithm for the l ...
... Decidability and Undecidability results Theorem. It is undecidable whether a first order logic formula is valid. Proof. Suppose there is an algorithm P that, given a first order logic and a formula in that logic, decides whether that formula is valid. We use P to give a decision algorithm for the l ...
A course in Mathematical Logic
... Terms and formulas are interpreted in a model. Definition 8. (Definition of a model) Let L be a language. An L-model M is given by a set M of elements (called the universe of the model) and 1. For every function symbol f ∈ L of arity n, a function f M : M n → M ; 2. For every relation symbol R ∈ L o ...
... Terms and formulas are interpreted in a model. Definition 8. (Definition of a model) Let L be a language. An L-model M is given by a set M of elements (called the universe of the model) and 1. For every function symbol f ∈ L of arity n, a function f M : M n → M ; 2. For every relation symbol R ∈ L o ...
Propositional Logic What is logic? Propositions Negation
... Let F(x) be the predicate “x is female”. Let P(x) be the predicate “x is a parent”. Let M(x,y) be the predicate “x is the mother of y”. Let the universe of discourse be the set of all people. We can express the statement “If a person is female and is a parent, then this person is someone’s mother”. ...
... Let F(x) be the predicate “x is female”. Let P(x) be the predicate “x is a parent”. Let M(x,y) be the predicate “x is the mother of y”. Let the universe of discourse be the set of all people. We can express the statement “If a person is female and is a parent, then this person is someone’s mother”. ...
A Proof Theory for Generic Judgments
... instead. In natural deduction and sequent calculus proofs, such new variables are called eigenvariables, and they are used to prove universally quantified formulas generically. In Gentzen’s original presentation of the sequent calculus [Gentzen 1969], eigenvariables were immutable: once an eigenvari ...
... instead. In natural deduction and sequent calculus proofs, such new variables are called eigenvariables, and they are used to prove universally quantified formulas generically. In Gentzen’s original presentation of the sequent calculus [Gentzen 1969], eigenvariables were immutable: once an eigenvari ...
S2 - CALCULEMUS.ORG
... result, until the questions and problems concerning researches on the foundations of computer science arose, most of the mathematicians did not pay too much attention to semantics restricted to finite models. The most extreme example of this is the monograph [Chang – Keisler 1990] reassuming some im ...
... result, until the questions and problems concerning researches on the foundations of computer science arose, most of the mathematicians did not pay too much attention to semantics restricted to finite models. The most extreme example of this is the monograph [Chang – Keisler 1990] reassuming some im ...
Linear Contextual Modal Type Theory
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
KnotandTonk 1 Preliminaries
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
Proof Theory: From Arithmetic to Set Theory
... • Logic as we know it today has only emerged over the past 140 years. • Chiefly associated with this emergence is Gottlob Frege (1848–1925). In his Begriffsschrift 1879 (Concept Script) he invented the first programming language. • His Begriffsschrift marked a turning point in the history of logic. ...
... • Logic as we know it today has only emerged over the past 140 years. • Chiefly associated with this emergence is Gottlob Frege (1848–1925). In his Begriffsschrift 1879 (Concept Script) he invented the first programming language. • His Begriffsschrift marked a turning point in the history of logic. ...