A Complexity of Two-variable Logic on Finite Trees
... As mentioned in the introduction, satisfiability of the modal language XPath has been heavily studied, beginning with the work of Marx [Marx 2004] and Marx and de Rijke [Marx and de Rijke 2004]. A survey of some later results can be found in [Benedikt and Koch 2008]. Given that the translation from ...
... As mentioned in the introduction, satisfiability of the modal language XPath has been heavily studied, beginning with the work of Marx [Marx 2004] and Marx and de Rijke [Marx and de Rijke 2004]. A survey of some later results can be found in [Benedikt and Koch 2008]. Given that the translation from ...
Propositional inquisitive logic: a survey
... questions capture logical dependencies. The relation of dependency is also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in detail in [7]. In the propositional setting, full translations are p ...
... questions capture logical dependencies. The relation of dependency is also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in detail in [7]. In the propositional setting, full translations are p ...
On Decidability of Intuitionistic Modal Logics
... Intuitionistic modal logics arise naturally in many areas, in particular in computer science. Intuitionistic logic is a natural underlying logic when dealing with functions and types, and modalities may correspond to various computational phenomena like termination etc., see for example [8,3,2]. The ...
... Intuitionistic modal logics arise naturally in many areas, in particular in computer science. Intuitionistic logic is a natural underlying logic when dealing with functions and types, and modalities may correspond to various computational phenomena like termination etc., see for example [8,3,2]. The ...
Decision procedures in Algebra and Logic
... Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field instead of a commutative ring. • Jordan algebra: a Jordan ring except that R is a field. • Lie algebra: an algebra over a field respecting the Jacobi identity, whose vector multiplication, the Lie bracket ...
... Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field instead of a commutative ring. • Jordan algebra: a Jordan ring except that R is a field. • Lie algebra: an algebra over a field respecting the Jacobi identity, whose vector multiplication, the Lie bracket ...
Relevant deduction
... truth of this thesis by more profound logical means, and the first step towards this end was of course to explicate Hume’s thesis within a logical language. What is meant by a statement about ‘is’ and one about ‘ought’? The prima facie most plausible explication of Hume’s thesis was first suggested ...
... truth of this thesis by more profound logical means, and the first step towards this end was of course to explicate Hume’s thesis within a logical language. What is meant by a statement about ‘is’ and one about ‘ought’? The prima facie most plausible explication of Hume’s thesis was first suggested ...
page 139 MINIMIZING AMBIGUITY AND
... understandable). We should also take into account that the required precision is dependent on the actual text or theory we are dealing with. The classical view is right in that the formalization of our premises could be more precise. For instance: if we formalize the word “chair”, we should make use ...
... understandable). We should also take into account that the required precision is dependent on the actual text or theory we are dealing with. The classical view is right in that the formalization of our premises could be more precise. For instance: if we formalize the word “chair”, we should make use ...
pdf
... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
Intermediate Logic
... almost every mathematical object can be seen as a set of some kind. In logic, as in other parts of mathematics, sets and set theoretical talk is ubiquitous. So it will be important to discuss what sets are, and introduce the notations necessary to talk about sets and operations on sets in a standard ...
... almost every mathematical object can be seen as a set of some kind. In logic, as in other parts of mathematics, sets and set theoretical talk is ubiquitous. So it will be important to discuss what sets are, and introduce the notations necessary to talk about sets and operations on sets in a standard ...
pdf [local copy]
... little bearing on the description elimination process as a whole. However, we will see that this is not true. There are ‘good’ choices of paraphrase that guarantee that description elimination does always terminate, independent of the order in which descriptions are eliminated and what scopes are ch ...
... little bearing on the description elimination process as a whole. However, we will see that this is not true. There are ‘good’ choices of paraphrase that guarantee that description elimination does always terminate, independent of the order in which descriptions are eliminated and what scopes are ch ...
On the Expressive Power of QLTL⋆
... QLT L extends LT L by quantifications over atomic propositions. While the expressive power of LT L and its fragments have been made relatively clear, there are few results on the expressive power of QLT L and its fragments (besides those of LT L). A well-known result is that ω-regular languages can ...
... QLT L extends LT L by quantifications over atomic propositions. While the expressive power of LT L and its fragments have been made relatively clear, there are few results on the expressive power of QLT L and its fragments (besides those of LT L). A well-known result is that ω-regular languages can ...
Commonsense Reasoning by Integrating Simulation and Logic
... and Semantic Web reasoning. A thorough overview of the method and applications to reasoning with propositional, first order, modal, description and other logics can be found in D’Agostino et al.’s (eds) handbook [11] or other standard references for formal computer science. For convenience, we prese ...
... and Semantic Web reasoning. A thorough overview of the method and applications to reasoning with propositional, first order, modal, description and other logics can be found in D’Agostino et al.’s (eds) handbook [11] or other standard references for formal computer science. For convenience, we prese ...
Proofs
... An argument is said to be valid if whenever all the premises are true, the conclusion is also true. If the premises are true, but the conclusion false, the argument is said to be invalid. ...
... An argument is said to be valid if whenever all the premises are true, the conclusion is also true. If the premises are true, but the conclusion false, the argument is said to be invalid. ...
Insights into Modal Slash Logic and Modal Decidability
... is a finite set of variables, with x ∈ / W . We agree to write ∃x for (∃x/∅). If x1 , . . . , xn are pairwise distinct variables, we allow writing (∃x/x1 , . . . , xn ) for (∃x/{x1 , . . . , xn }). Expressions produced by the grammar are termed FOsL[τ ] strings. We may wish to distinguish two kinds ...
... is a finite set of variables, with x ∈ / W . We agree to write ∃x for (∃x/∅). If x1 , . . . , xn are pairwise distinct variables, we allow writing (∃x/x1 , . . . , xn ) for (∃x/{x1 , . . . , xn }). Expressions produced by the grammar are termed FOsL[τ ] strings. We may wish to distinguish two kinds ...
Beginning Logic - University of Notre Dame
... We will define what it means for a statement in a propositional or predicate language to be true in an appropriate formal setting. To show that an argument is not valid, we will look for a “counter-example”, a setting in which the premises are all true and the conclusion is false. IV. Analysis of ar ...
... We will define what it means for a statement in a propositional or predicate language to be true in an appropriate formal setting. To show that an argument is not valid, we will look for a “counter-example”, a setting in which the premises are all true and the conclusion is false. IV. Analysis of ar ...
Modal Logic for Artificial Intelligence
... valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . then’ and ‘if, and only if’, they are the logical constants of propositional logic (see section 1). A formal logic is a definition of valid argument forms, such as the one above. There are different methods for d ...
... valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . then’ and ‘if, and only if’, they are the logical constants of propositional logic (see section 1). A formal logic is a definition of valid argument forms, such as the one above. There are different methods for d ...
HKT Chapters 1 3
... when thinking of them as an algebraic structure with arithmetic operations + and · and the latter when thinking of them as the set of finite ordinal numbers. We reserve the symbols i, j, k, m, n to denote natural numbers. We use the symbols =⇒, → for implication (if-then) and ⇐⇒, ↔ for bidirectional ...
... when thinking of them as an algebraic structure with arithmetic operations + and · and the latter when thinking of them as the set of finite ordinal numbers. We reserve the symbols i, j, k, m, n to denote natural numbers. We use the symbols =⇒, → for implication (if-then) and ⇐⇒, ↔ for bidirectional ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn
... Aristotle observed that the correctness of this inference has nothing to do with the truth or falsity of the individual statements, but, rather, the general pattern: Every A is B. Every B is C. Therefore every A is C. We can substitute various properties for A, B, and C; try substituting the propert ...
... Aristotle observed that the correctness of this inference has nothing to do with the truth or falsity of the individual statements, but, rather, the general pattern: Every A is B. Every B is C. Therefore every A is C. We can substitute various properties for A, B, and C; try substituting the propert ...
Connecting a Logical Framework to a First
... to this fragment, we can use the idea of implicit typing [Bee05,WM89]. In this way, the translation from framework types to FOL formulæ is particularly simple. Technically, this is reflected by a general meta-theorem which ensures that we can lift a first-order resolution proof to a framework deriva ...
... to this fragment, we can use the idea of implicit typing [Bee05,WM89]. In this way, the translation from framework types to FOL formulæ is particularly simple. Technically, this is reflected by a general meta-theorem which ensures that we can lift a first-order resolution proof to a framework deriva ...
A pragmatic dialogic interpretation of bi
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
Proofs in Propositional Logic
... interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lead to verbose developments (remember that the user has to type the sta ...
... interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lead to verbose developments (remember that the user has to type the sta ...
Proofs in Propositional Logic
... interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lead to verbose developments (remember that the user has to type the sta ...
... interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lead to verbose developments (remember that the user has to type the sta ...
On the Complexity of Resolution-based Proof Systems
... the length of proofs in propositional logic. One of its main questions is to determine which particular propositional formulas have short proofs in a given propositional proof system. In this thesis we present several results related to this question, all on proof systems that are extensions of the ...
... the length of proofs in propositional logic. One of its main questions is to determine which particular propositional formulas have short proofs in a given propositional proof system. In this thesis we present several results related to this question, all on proof systems that are extensions of the ...
TSTP Data-Exchange Formats for Automated Theorem Proving Tools
... As ATP systems move into real application areas, they are typically embedded as just one component in a larger system, including tools for proof analysis, transformation, presentation, and verification. In this environment, the output from one tool is often used as input to another. It is therefore ...
... As ATP systems move into real application areas, they are typically embedded as just one component in a larger system, including tools for proof analysis, transformation, presentation, and verification. In this environment, the output from one tool is often used as input to another. It is therefore ...
11. Predicate Logic Syntax and Semantics, Normal Forms, Herbrand
... us to determine satisfiability or general validity (by transformation into DNF or CNF). But: we can reduce the satisfiability problem in predicate logic to the satisfiability problem in propositional logic. In general, however, this produces a very large number of propositional formulae (perhaps inf ...
... us to determine satisfiability or general validity (by transformation into DNF or CNF). But: we can reduce the satisfiability problem in predicate logic to the satisfiability problem in propositional logic. In general, however, this produces a very large number of propositional formulae (perhaps inf ...