slides
... Want a way to prove partial correctness statements valid... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional ...
... Want a way to prove partial correctness statements valid... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional ...
Logic: Introduction - Department of information engineering and
... Modern Logic teaches us that one claim is a logical consequence of another if there is no way the latter could be true without the former also being true. It is also used to disconfirm a theory if a particular claim is a logical consequence of a theory, and we discover that the claim is false, then ...
... Modern Logic teaches us that one claim is a logical consequence of another if there is no way the latter could be true without the former also being true. It is also used to disconfirm a theory if a particular claim is a logical consequence of a theory, and we discover that the claim is false, then ...
Logic I Fall 2009 Problem Set 5
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
Solutions to Problem Set 1
... Finally, we can say there is some student who emailed exactly two other two students by existentially quantifying x, y and z. So the complete translation is ∃x∃y∃z. E(x, y) ∧ E(x, z)∧ � y∧x= � z∧y = � z∧ x= ∀s, E(x, s) −→ s = x ∨ s = y ∨ s = z. ...
... Finally, we can say there is some student who emailed exactly two other two students by existentially quantifying x, y and z. So the complete translation is ∃x∃y∃z. E(x, y) ∧ E(x, z)∧ � y∧x= � z∧y = � z∧ x= ∀s, E(x, s) −→ s = x ∨ s = y ∨ s = z. ...
A BRIEF INTRODUCTION TO MODAL LOGIC Introduction Consider
... will be true in this world. The more interesting case comes with our new operators, and ♦. P is defined to be true in a world whenever P is true in all ‘accessible’ worlds. How we define accessibility depends on the modality, but ‘conceivable’ is a common one for the necessary/possible modality. ...
... will be true in this world. The more interesting case comes with our new operators, and ♦. P is defined to be true in a world whenever P is true in all ‘accessible’ worlds. How we define accessibility depends on the modality, but ‘conceivable’ is a common one for the necessary/possible modality. ...
Notes on Classical Propositional Logic
... 2. Every rule is sound, which means that any boolean valuation that maps all the premises of a rule application to true must also map the conclusion of the rule to true. Then the axiom system is sound; it only proves tautologies. Proof It is easy to see that if the conditions are met, every line of ...
... 2. Every rule is sound, which means that any boolean valuation that maps all the premises of a rule application to true must also map the conclusion of the rule to true. Then the axiom system is sound; it only proves tautologies. Proof It is easy to see that if the conditions are met, every line of ...
Intuitionistic modal logic made explicit
... sense and introduced epistemic, i.e., possible world, models for justification logics. These models have been further developed to modular models as we use them in this paper [5, 17]. This general reading of justification led to many applications in epistemic logic [3, 4, 7, 8, 9, 10, 14, 16, 18]. G ...
... sense and introduced epistemic, i.e., possible world, models for justification logics. These models have been further developed to modular models as we use them in this paper [5, 17]. This general reading of justification led to many applications in epistemic logic [3, 4, 7, 8, 9, 10, 14, 16, 18]. G ...
An Automata Theoretic Decision Procedure for the Propositional Mu
... Fischer and Ladner (1979). Kozen’s formulation captures the infinite looping construct of Streett (1982) and subsumes Parikh’s game logic (1983a, 1983b), whereas Pratt’s logic is designed to express the converse operator of PDL. The filtration-based decision procedure and small model theorem obtaine ...
... Fischer and Ladner (1979). Kozen’s formulation captures the infinite looping construct of Streett (1982) and subsumes Parikh’s game logic (1983a, 1983b), whereas Pratt’s logic is designed to express the converse operator of PDL. The filtration-based decision procedure and small model theorem obtaine ...
`A` now that you can cheat sheet
... You all better get an ‘A’ now that you can cheat sheet Arguments An argument is valid (or logical) if the conclusion is supported by the premises An argument is deductively valid if the truth of the premises guarantee the truth of the conclusion (i.e. if it is impossible for the conclusion to be fal ...
... You all better get an ‘A’ now that you can cheat sheet Arguments An argument is valid (or logical) if the conclusion is supported by the premises An argument is deductively valid if the truth of the premises guarantee the truth of the conclusion (i.e. if it is impossible for the conclusion to be fal ...
Lecture Notes 2
... mathematicians, is just as rigorous. It consists of sentences describing the situation at hand, the inferences being made, and the justification of each inference. ...
... mathematicians, is just as rigorous. It consists of sentences describing the situation at hand, the inferences being made, and the justification of each inference. ...
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 : ...