Guarded negation
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
Logic and Resolution - Institute for Computing and Information
... The notion of well-formedness of formulas only concerns the syntax of formulas in propositional logic: it does not express the formulas to be either true or false. In other words, it tells us nothing with respect to the semantics or meaning of formulas in propositional logic. The truth or falsity of ...
... The notion of well-formedness of formulas only concerns the syntax of formulas in propositional logic: it does not express the formulas to be either true or false. In other words, it tells us nothing with respect to the semantics or meaning of formulas in propositional logic. The truth or falsity of ...
Chapter 1 Logic
... An example of using a universal quantifier is: “for all integers n, the integer n(n + 1) is even”. We could take a first step towards a symbolic representation of this statement by writing “∀n, n(n+1) is even”, and specifying that the universe of n is the integers. (This statement is true.) The exis ...
... An example of using a universal quantifier is: “for all integers n, the integer n(n + 1) is even”. We could take a first step towards a symbolic representation of this statement by writing “∀n, n(n+1) is even”, and specifying that the universe of n is the integers. (This statement is true.) The exis ...
Bounded Proofs and Step Frames - Università degli Studi di Milano
... principle and elements from Γ as well as modus ponens, necessitation and inferences from Ax (again notice that uniform substitution cannot be applied to members of Γ ). We need some care when replacing a logic L with an inference system Ax, because we want global consequence relation to be preserve ...
... principle and elements from Γ as well as modus ponens, necessitation and inferences from Ax (again notice that uniform substitution cannot be applied to members of Γ ). We need some care when replacing a logic L with an inference system Ax, because we want global consequence relation to be preserve ...
Lecture slides
... To say that an argument form is valid means that if the substituted statements result in valid premises, then the conclusion is also true. Here the two premises are: If p then q p The truth of the conclusion is said to be inferred from or deduced from the truth of the premises. If statements substit ...
... To say that an argument form is valid means that if the substituted statements result in valid premises, then the conclusion is also true. Here the two premises are: If p then q p The truth of the conclusion is said to be inferred from or deduced from the truth of the premises. If statements substit ...
Proof Search in Modal Logic
... and the Logic of Provability (GL). An intercalation calculus ([10]) was used as the underlying logical calculus, and the proof search was automated using the theorem prover AProS [1]. The inference rules in the intercalation calculus for the systems S5 and GL, and their soundness and completeness re ...
... and the Logic of Provability (GL). An intercalation calculus ([10]) was used as the underlying logical calculus, and the proof search was automated using the theorem prover AProS [1]. The inference rules in the intercalation calculus for the systems S5 and GL, and their soundness and completeness re ...
Modal Logic for Artificial Intelligence
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
File
... judicious combination of all the above methods of naming techniques is used throughout this course to describe the language structure. Now we are in a convenient position to write the statement. (11) “ Haritha is clever “is true. (12) (7) is true. The above representation is confirmed with accepted ...
... judicious combination of all the above methods of naming techniques is used throughout this course to describe the language structure. Now we are in a convenient position to write the statement. (11) “ Haritha is clever “is true. (12) (7) is true. The above representation is confirmed with accepted ...
Interpreting and Applying Proof Theories for Modal Logic
... 4 Note that from now on the operator will not be taken as primitive but as defined in the following standard way: A = ¬¬A, not because it couldn’t be primitive, but for compactnesss of presentation. 5 In Belnap’s original work on Display Logic, the modal operators are treated with another family ...
... 4 Note that from now on the operator will not be taken as primitive but as defined in the following standard way: A = ¬¬A, not because it couldn’t be primitive, but for compactnesss of presentation. 5 In Belnap’s original work on Display Logic, the modal operators are treated with another family ...
Completeness in modal logic - Lund University Publications
... devised to give formal accounts of the idea that propositions may not merely be true or false, but necessarily true/false, or false yet possibly true etc. Essential to modal logics is the addition of the operators “ ” (for necessity) and “◊” (for possibility) to the language. ...
... devised to give formal accounts of the idea that propositions may not merely be true or false, but necessarily true/false, or false yet possibly true etc. Essential to modal logics is the addition of the operators “ ” (for necessity) and “◊” (for possibility) to the language. ...
article in press - School of Computer Science
... relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which involve more than one guard relation. We believe that this method is particularly promisi ...
... relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which involve more than one guard relation. We believe that this method is particularly promisi ...
true - DoguAkdeniz.Com
... The conditional expression is evaluated by first evaluating the expression_1. If the resultant value is nonzero (true), then the expression_2 is evaluated and its value become the overall result. Otherwise, the expression_3 is evaluated, and its value becomes the result This operator is most oft ...
... The conditional expression is evaluated by first evaluating the expression_1. If the resultant value is nonzero (true), then the expression_2 is evaluated and its value become the overall result. Otherwise, the expression_3 is evaluated, and its value becomes the result This operator is most oft ...
ON PRESERVING 1. Introduction The
... It’s consistency itself, or at least many accounts of it, which casts a shadow over our everyday logical doings. The way we have set things up, a set Γ of formulas is either consistent in a logic X, or it isn’t. But it doesn’t take much thought to see that such an all-or-nothing approach tramples so ...
... It’s consistency itself, or at least many accounts of it, which casts a shadow over our everyday logical doings. The way we have set things up, a set Γ of formulas is either consistent in a logic X, or it isn’t. But it doesn’t take much thought to see that such an all-or-nothing approach tramples so ...
Kripke completeness revisited
... relation, as those needed in temporal logic, the canonical accessibility relation need not be irreflexive; Some extra devices, such as the one called bulldozing have to be used to obtain an irreflexive frame from the canonical one (cf. Bull and Segerberg 1984, 2001). The criticism of insufficient fo ...
... relation, as those needed in temporal logic, the canonical accessibility relation need not be irreflexive; Some extra devices, such as the one called bulldozing have to be used to obtain an irreflexive frame from the canonical one (cf. Bull and Segerberg 1984, 2001). The criticism of insufficient fo ...
Systems of modal logic - Department of Computing
... In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Whi ...
... In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Whi ...
A course in Mathematical Logic
... To know the truth value of the propositional formula (A ∧ B) → C, we need to know the truth values of the propositional variables A, B, C. For example, if A, C are true and B is false, then (A ∧ B) → C is true. The formula A ∧ B is false because B is false, and any implication, whose premises is fa ...
... To know the truth value of the propositional formula (A ∧ B) → C, we need to know the truth values of the propositional variables A, B, C. For example, if A, C are true and B is false, then (A ∧ B) → C is true. The formula A ∧ B is false because B is false, and any implication, whose premises is fa ...
On Decidability of Intuitionistic Modal Logics
... τx (ϕ ⇒ ψ) := ∀y(R(x, y) → (¬τy (ϕ) ∨ τy (ψ))) τx (2ϕ) := ∀y(R(x, y) → ∀x(R2 (y, x) → τx (ϕ))) τx (3ϕ) := ∀y(R(x, y) → ∃x(R3 (y, x) ∧ τx (ϕ))) τy is defined analogously, switching the roles of x and y. This translation assumes modal truth clauses (22 ) and (32 ). Clauses for (21 ) and (31 ) are even ...
... τx (ϕ ⇒ ψ) := ∀y(R(x, y) → (¬τy (ϕ) ∨ τy (ψ))) τx (2ϕ) := ∀y(R(x, y) → ∀x(R2 (y, x) → τx (ϕ))) τx (3ϕ) := ∀y(R(x, y) → ∃x(R3 (y, x) ∧ τx (ϕ))) τy is defined analogously, switching the roles of x and y. This translation assumes modal truth clauses (22 ) and (32 ). Clauses for (21 ) and (31 ) are even ...
Counterfactuals
... (^) which behaves as a restricted existential quantification over accessible worlds; some sentence φ is true if and only if there exists some world where φ is true which is accessible from the base world. As with necessity, what worlds are regarded as accessible is meant to be varied depending on th ...
... (^) which behaves as a restricted existential quantification over accessible worlds; some sentence φ is true if and only if there exists some world where φ is true which is accessible from the base world. As with necessity, what worlds are regarded as accessible is meant to be varied depending on th ...