First-Order Theorem Proving and Vampire
... Which of the following statements are true? 1. First-order logic is an extension of propositional logic; 2. First-order logic is NP-complete. 3. First-order logic is PSPACE-complete. 4. First-order logic is decidable. 5. In first-order logic you can use quantifiers over sets. 6. One can axiomatise i ...
... Which of the following statements are true? 1. First-order logic is an extension of propositional logic; 2. First-order logic is NP-complete. 3. First-order logic is PSPACE-complete. 4. First-order logic is decidable. 5. In first-order logic you can use quantifiers over sets. 6. One can axiomatise i ...
QUASI-MV ALGEBRAS. PART III
... at least one fixpoint for ′ , namely, the unique regular member of C. If any other fixpoints exist, they also belong to C. We choose arbitrarily some maximal set S of clouds that contains at most one of each pair of twin clouds. In particular, the median cloud is not a member of S, but, by maximality, ...
... at least one fixpoint for ′ , namely, the unique regular member of C. If any other fixpoints exist, they also belong to C. We choose arbitrarily some maximal set S of clouds that contains at most one of each pair of twin clouds. In particular, the median cloud is not a member of S, but, by maximality, ...
Principia Logico-Metaphysica (Draft/Excerpt)
... In this and subsequent chapters, our metalanguage makes use of informal notions and principles about numbers and sets so as to more precisely articulate and render certain definitions. These are not primitive notions or principles of our metaphysical system; ultimately, they are to be understood by ...
... In this and subsequent chapters, our metalanguage makes use of informal notions and principles about numbers and sets so as to more precisely articulate and render certain definitions. These are not primitive notions or principles of our metaphysical system; ultimately, they are to be understood by ...
Saying It with Pictures: a logical landscape of conceptual graphs
... the success of visual information in human communication and exploiting them in an automated fashion has gained a prominent place in the artificial intelligence agenda. By considering several aspects of graphical languages in knowledge representation, this thesis positions conceptual graphs, a specifi ...
... the success of visual information in human communication and exploiting them in an automated fashion has gained a prominent place in the artificial intelligence agenda. By considering several aspects of graphical languages in knowledge representation, this thesis positions conceptual graphs, a specifi ...
m - Arie Gurfinkel
... An alternative is to let m0 be an implicant (not necessarily prime) of FiÆ9 X’.(Tr Æ m’) • finding a prime implicant is difficult because of the existential quantification • we settle for an arbitrary implicant. The side conditions ensure it is not trivial Building Verifiers from Comp and SMT Gurfin ...
... An alternative is to let m0 be an implicant (not necessarily prime) of FiÆ9 X’.(Tr Æ m’) • finding a prime implicant is difficult because of the existential quantification • we settle for an arbitrary implicant. The side conditions ensure it is not trivial Building Verifiers from Comp and SMT Gurfin ...
Labeled Natural Deduction for Temporal Logics
... 1.1 Background and motivation The history of the philosophical and logical reasoning about time goes back at least to ancient Greece, with the works of Aristotle and Diodorus Cronus. However, the birth of modern (symbolic) temporal logic is mainly connected to the name of Prior, who in the late 1950 ...
... 1.1 Background and motivation The history of the philosophical and logical reasoning about time goes back at least to ancient Greece, with the works of Aristotle and Diodorus Cronus. However, the birth of modern (symbolic) temporal logic is mainly connected to the name of Prior, who in the late 1950 ...
A Unified View of Induction Reasoning for First-Order Logic
... for example, a positive clause φ is an inductive consequence of a set of universally quantified Horn clauses with equality iff φ is valid in their initial model [24]. A formula φ is false, denoted by 6|=M φ, if it is not valid. Any false formula has (or contains) at least one false ground instance, ...
... for example, a positive clause φ is an inductive consequence of a set of universally quantified Horn clauses with equality iff φ is valid in their initial model [24]. A formula φ is false, denoted by 6|=M φ, if it is not valid. Any false formula has (or contains) at least one false ground instance, ...
Structural Proof Theory
... the same as the logical task of controlling the correctness of a formal proof. We do not cover constructive type theory in detail, as another book would be needed for that, but some of the basic ideas and their connection to natural deduction and normalization procedures are explained in Appendix B. ...
... the same as the logical task of controlling the correctness of a formal proof. We do not cover constructive type theory in detail, as another book would be needed for that, but some of the basic ideas and their connection to natural deduction and normalization procedures are explained in Appendix B. ...
Color - Alex Kocurek
... However, even with possibilist quantifiers and the actuality operator, sentences like the following seem to remain inexpressible:6 (NR) Necessarily, everyone who’s rich could have been poor. One could try to fix this problem by adding more and more operators to the language, some of which we will di ...
... However, even with possibilist quantifiers and the actuality operator, sentences like the following seem to remain inexpressible:6 (NR) Necessarily, everyone who’s rich could have been poor. One could try to fix this problem by adding more and more operators to the language, some of which we will di ...
Goal-directed Proof Theory
... community. There are those members who believe that the new non-classical logics are the most important ones for applications and that classical logic itself is now no longer the main workhorse of applied logic and there are those who maintain that classical logic is the only logic worth considering ...
... community. There are those members who believe that the new non-classical logics are the most important ones for applications and that classical logic itself is now no longer the main workhorse of applied logic and there are those who maintain that classical logic is the only logic worth considering ...
Announcement as effort on topological spaces
... x (Moss and Parikh, 1992). According to subset space semantics, given a pair (x, U ), the modality K quantifies over the elements of U , whereas 2 quantifies over all subsets of U in O that include the actual world x. Therefore, while knowledge is interpreted ‘locally’ in a given turthful observatio ...
... x (Moss and Parikh, 1992). According to subset space semantics, given a pair (x, U ), the modality K quantifies over the elements of U , whereas 2 quantifies over all subsets of U in O that include the actual world x. Therefore, while knowledge is interpreted ‘locally’ in a given turthful observatio ...
Proofs in Propositional Logic
... The basic tool for interactively solving a goal G =Γ A is called a tactic, which is a command typed by the user. An elementary step of an interactive proof has the following form : The user tries to apply a tactic to (by default) the first ...
... The basic tool for interactively solving a goal G =Γ A is called a tactic, which is a command typed by the user. An elementary step of an interactive proof has the following form : The user tries to apply a tactic to (by default) the first ...
Proofs in Propositional Logic
... The basic tool for interactively solving a goal G =Γ A is called a tactic, which is a command typed by the user. An elementary step of an interactive proof has the following form : The user tries to apply a tactic to (by default) the first ...
... The basic tool for interactively solving a goal G =Γ A is called a tactic, which is a command typed by the user. An elementary step of an interactive proof has the following form : The user tries to apply a tactic to (by default) the first ...
MARTIN`S CONJECTURE, ARITHMETIC EQUIVALENCE, AND
... The first progress on Martin’s conjecture was made by Steel [26] and was continued by Slaman and Steel [25]. They proved that Martin’s conjecture is true when restricted to the class of uniformly Turing invariant functions. Theorem 1.2 (Slaman and Steel [25]). Part I of Martin’s conjecture holds for ...
... The first progress on Martin’s conjecture was made by Steel [26] and was continued by Slaman and Steel [25]. They proved that Martin’s conjecture is true when restricted to the class of uniformly Turing invariant functions. Theorem 1.2 (Slaman and Steel [25]). Part I of Martin’s conjecture holds for ...
AN EARLY HISTORY OF MATHEMATICAL LOGIC AND
... or Richard Dedekind. I believe this is because Styazhkin believes first, that logic from Leibniz to Peano was largely separate from set theory; and second, he believed that logic after Peano changed radically in its relationship with set theory. This is just the view that I want to combat. The reaso ...
... or Richard Dedekind. I believe this is because Styazhkin believes first, that logic from Leibniz to Peano was largely separate from set theory; and second, he believed that logic after Peano changed radically in its relationship with set theory. This is just the view that I want to combat. The reaso ...
SEQUENT SYSTEMS FOR MODAL LOGICS
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
logic, programming and prolog (2ed)
... most elaborate theorems are stated only with hints or pointers to their proofs; • most of the program examples are small programs whose prime aim is to illustrate the principal use of logic programming and to inspire the reader to apply similar techniques when writing “real” logic programs. ...
... most elaborate theorems are stated only with hints or pointers to their proofs; • most of the program examples are small programs whose prime aim is to illustrate the principal use of logic programming and to inspire the reader to apply similar techniques when writing “real” logic programs. ...
Logic in Nonmonotonic Reasoning
... logical and causal properties of a situation. Suppose we have a suitcase with two locks, and it is opened if both locks are open. Then the action of opening one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into a ...
... logical and causal properties of a situation. Suppose we have a suitcase with two locks, and it is opened if both locks are open. Then the action of opening one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into a ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... The Calculus NJ of Natural Deduction (Propositional Part) ...
... The Calculus NJ of Natural Deduction (Propositional Part) ...
Some Aspects and Examples of In nity Notions T ZF
... which does not possess any in nite branch. So let such a tree be given, and denote by x the set of its points. If we assign the root to the root and to each other point its father the we get in this way a noninjective surjection of x onto x . Hence the set x is dually Dedekind-in nite. Now we show ...
... which does not possess any in nite branch. So let such a tree be given, and denote by x the set of its points. If we assign the root to the root and to each other point its father the we get in this way a noninjective surjection of x onto x . Hence the set x is dually Dedekind-in nite. Now we show ...
Ribbon Proofs - A Proof System for the Logic of Bunched Implications
... Syntactic proof systems for formal logics fall into some broad categories. Perhaps the simplest in presentation are the Hilbert-style systems[21]. A Hilbert system consists of a number of logical formulae accepted to be fundamentally true (axioms) and a number of rules allowing deductions of new for ...
... Syntactic proof systems for formal logics fall into some broad categories. Perhaps the simplest in presentation are the Hilbert-style systems[21]. A Hilbert system consists of a number of logical formulae accepted to be fundamentally true (axioms) and a number of rules allowing deductions of new for ...
Abella: A System for Reasoning about Relational Specifications
... font: in addition, keywords are depicted in blue. The types, terms, and formulas used by Abella are described briefly below as well as in the table in Figure 1. Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The ...
... font: in addition, keywords are depicted in blue. The types, terms, and formulas used by Abella are described briefly below as well as in the table in Figure 1. Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The ...
Reading
... is, strictly speaking, a distinct principle from HP, since HP = AX≈Y and HP2 = AY≈X (further, neither HP → HP2 nor HP2 → HP is a logical truth, since HP and HP2 involve distinct abstraction operators @X≈Y and @Y≈X). We shall address subtle issues regarding the equivalence of abstraction principles b ...
... is, strictly speaking, a distinct principle from HP, since HP = AX≈Y and HP2 = AY≈X (further, neither HP → HP2 nor HP2 → HP is a logical truth, since HP and HP2 involve distinct abstraction operators @X≈Y and @Y≈X). We shall address subtle issues regarding the equivalence of abstraction principles b ...
The Z/EVES 2.0 User`s Guide - Department of Computer Science
... selected paragraph or paragraphs to be inserted immediately before the selected location. The move can be canceled by right clicking, then selecting “Cancel” from the pop-up menu. Paragraph order is important. A Z specification is a sequence of paragraphs and requires declaration before use. The ord ...
... selected paragraph or paragraphs to be inserted immediately before the selected location. The move can be canceled by right clicking, then selecting “Cancel” from the pop-up menu. Paragraph order is important. A Z specification is a sequence of paragraphs and requires declaration before use. The ord ...
Hilbert`s Program Then and Now
... these objects must be capable of being completely surveyed in all their parts, and their presentation, their difference, their succession (like the objects themselves) must exist for us immediately, intuitively, as something which cannot be reduced to something else.4 The objects in questions are si ...
... these objects must be capable of being completely surveyed in all their parts, and their presentation, their difference, their succession (like the objects themselves) must exist for us immediately, intuitively, as something which cannot be reduced to something else.4 The objects in questions are si ...