Deep Sequent Systems for Modal Logic
... the ability to apply rules deep inside of a formula. So far the calculus of structures has captured essentially those modal logics which can also be captured using the sequent calculus or hypersequents. In particular that does not include B and K5. It turns out that not all the depth of the calculus ...
... the ability to apply rules deep inside of a formula. So far the calculus of structures has captured essentially those modal logics which can also be captured using the sequent calculus or hypersequents. In particular that does not include B and K5. It turns out that not all the depth of the calculus ...
Automata vs. Logics on Data Words
... MSO(∼, <) denotes monadic second-order logic with predicates ∼ and <, interpreted respectively by the data-equality relation and by the total order relation over the positions of a given data word. FO(∼, <) is the restriction of MSO(∼, <) that only uses quantification over first-order variables. An ...
... MSO(∼, <) denotes monadic second-order logic with predicates ∼ and <, interpreted respectively by the data-equality relation and by the total order relation over the positions of a given data word. FO(∼, <) is the restriction of MSO(∼, <) that only uses quantification over first-order variables. An ...
Modal Languages and Bounded Fragments of Predicate Logic
... standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from propositional modal logic with operators ♦ and , possibly indexed, into the first-order language over possible worlds models (van Benthem 197 ...
... standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from propositional modal logic with operators ♦ and , possibly indexed, into the first-order language over possible worlds models (van Benthem 197 ...
HPL-2008 - HP Labs
... Many access control systems live in an environment in which significant events occur simultaneously. Moreover, events of the access system itself may occur concurrently and there may be complex interactions between all parts of the system and the environment. A modelling framework that describes suc ...
... Many access control systems live in an environment in which significant events occur simultaneously. Moreover, events of the access system itself may occur concurrently and there may be complex interactions between all parts of the system and the environment. A modelling framework that describes suc ...
Chapter 4, Mathematics
... ‘algorithm’. For example the standard procedures for addition, subtraction and multiplication are all algorithms. In logical theory ‘decision procedure’ is equivalent to ‘algorithm’. In cookery a reliable recipe is an algorithm for producing the soup, cake, stew or whatever it is that it tells us ho ...
... ‘algorithm’. For example the standard procedures for addition, subtraction and multiplication are all algorithms. In logical theory ‘decision procedure’ is equivalent to ‘algorithm’. In cookery a reliable recipe is an algorithm for producing the soup, cake, stew or whatever it is that it tells us ho ...
Rules of inference
... This argument is of the form p q and q then p. This is an example of an incorrect argument using the Fallacy of affirming the conclusion. pq and q does not imply p. The proposition [(pq) q) p] is not a tautology (its false if p is F and q is T) check the truth table You can learn discrete mathe ...
... This argument is of the form p q and q then p. This is an example of an incorrect argument using the Fallacy of affirming the conclusion. pq and q does not imply p. The proposition [(pq) q) p] is not a tautology (its false if p is F and q is T) check the truth table You can learn discrete mathe ...
Math 318 Class notes
... we can form the set { X }. The empty set : ∅. Examples of sets: {∅}, {{∅}, {∅, {∅}}}. Extensionality property: two sets are equal iff they have the same elements. The formal axioms of Zermelo-Fraenkl set theory are presented later, in 9.5. To interpret natural numbers as sets, we adopt the conventio ...
... we can form the set { X }. The empty set : ∅. Examples of sets: {∅}, {{∅}, {∅, {∅}}}. Extensionality property: two sets are equal iff they have the same elements. The formal axioms of Zermelo-Fraenkl set theory are presented later, in 9.5. To interpret natural numbers as sets, we adopt the conventio ...
Let me begin by reminding you of a number of passages ranging
... that the notion of truth plays in logic that psychologism with respect to logic is exposed as bankrupt. As Frege points out in “Der Gedanke”, for example, when logical laws, the laws of being true, are assimilated to psychological laws of thinking, of taking to be true, “truth has not been given its ...
... that the notion of truth plays in logic that psychologism with respect to logic is exposed as bankrupt. As Frege points out in “Der Gedanke”, for example, when logical laws, the laws of being true, are assimilated to psychological laws of thinking, of taking to be true, “truth has not been given its ...
Programming with Classical Proofs
... µT which extends µ with natural numbers as a primitive datatype. These systems correspond to classical propositional logic, which means that their type systems are rather simple, and that, when they are equipped with datatypes, they are more closely related to real world computer programming languag ...
... µT which extends µ with natural numbers as a primitive datatype. These systems correspond to classical propositional logic, which means that their type systems are rather simple, and that, when they are equipped with datatypes, they are more closely related to real world computer programming languag ...
Heyting-valued interpretations for Constructive Set Theory
... formal topology and constructive set theories analogous to the one existing between locale theory and intuitionistic set theories. We do so by investigating Heyting-valued interpretations for the Constructive Zermelo-Frankel set theory, CZF [6]. The study of Heyting-valued interpretations reveals ma ...
... formal topology and constructive set theories analogous to the one existing between locale theory and intuitionistic set theories. We do so by investigating Heyting-valued interpretations for the Constructive Zermelo-Frankel set theory, CZF [6]. The study of Heyting-valued interpretations reveals ma ...
Complexity of Contextual Reasoning
... establishes NP-membership for PLC, but leaves MCS/LMS out of consideration. Serafini and Roelofsen (2004) provide a deterministic S AT-based decision procedure that applies to both MCS/LMS and PLC, but they do not consider the effect that introducing non-determinism may have on the inherent complexi ...
... establishes NP-membership for PLC, but leaves MCS/LMS out of consideration. Serafini and Roelofsen (2004) provide a deterministic S AT-based decision procedure that applies to both MCS/LMS and PLC, but they do not consider the effect that introducing non-determinism may have on the inherent complexi ...
Predicate logic. Formal and informal proofs
... Proving theorems in practice: • The steps of the proofs are not expressed in any formal language as e.g. propositional logic • Steps are argued less formally using English, mathematical formulas and so on • One must always watch the consistency of the argument made, logic and its rules can often hel ...
... Proving theorems in practice: • The steps of the proofs are not expressed in any formal language as e.g. propositional logic • Steps are argued less formally using English, mathematical formulas and so on • One must always watch the consistency of the argument made, logic and its rules can often hel ...
PROVING THE CORRECTNESS OF REGULA DETERMINISTIC
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...
Outline of Lecture 2 First Order Logic and Second Order Logic Basic
... The following graph properties are FOL-definable: • For H any simple graph, let F orbind(H) class of finite graphs which have no induced copy of H. • Cographs were first defined inductively: The class of cographs is the smallest class of graphs which contains the single vertex graph E1 and is closed ...
... The following graph properties are FOL-definable: • For H any simple graph, let F orbind(H) class of finite graphs which have no induced copy of H. • Cographs were first defined inductively: The class of cographs is the smallest class of graphs which contains the single vertex graph E1 and is closed ...
page 135 ADAPTIVE LOGICS FOR QUESTION EVOCATION
... In this section, I present an intuitive characterization of the dynamic proof theory of the logic Qs . I begin, however, with some remarks on the logic of questions Q on which Qs is based. The logic Q is an erotetic extension of (the ω-complete fragment of) CL, and is obtained by enriching the langu ...
... In this section, I present an intuitive characterization of the dynamic proof theory of the logic Qs . I begin, however, with some remarks on the logic of questions Q on which Qs is based. The logic Q is an erotetic extension of (the ω-complete fragment of) CL, and is obtained by enriching the langu ...
INTRODUCTION TO THE THEORY OF PROOFS 3A. The Gentzen
... Main part of the proof. We now consider cases on what the last left inference and the last right inference is, and we may assume that the Main Lemma holds for all cases of smaller grade, and for all cases of the same grade but smaller rank. The cases where one of the ranks is > 1 are treated first, ...
... Main part of the proof. We now consider cases on what the last left inference and the last right inference is, and we may assume that the Main Lemma holds for all cases of smaller grade, and for all cases of the same grade but smaller rank. The cases where one of the ranks is > 1 are treated first, ...
210ch2 - Dr. Djamel Bouchaffra
... Note: f associates with each x in A one and only one y in B. A is called the domain and B is called the codomain. If f(x) = y y is called the image of x under f x is called a preimage of y (note there may be more than one preimage of y but there is only one image of x). The range of f is the set of ...
... Note: f associates with each x in A one and only one y in B. A is called the domain and B is called the codomain. If f(x) = y y is called the image of x under f x is called a preimage of y (note there may be more than one preimage of y but there is only one image of x). The range of f is the set of ...
relevance logic - Consequently.org
... ways that writers on relevance logic often express themselves. We draw heavily on the ‘Grammatical Propaedeutic’ appendix of [Anderson and Belnap, 1975] and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus l ...
... ways that writers on relevance logic often express themselves. We draw heavily on the ‘Grammatical Propaedeutic’ appendix of [Anderson and Belnap, 1975] and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus l ...
