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 ...
slides
... defined the infinitary version of the logic of here-and-there, defined its nonmonotonic counterpart—the infinitary version of equilibrium logic, verified that stable models of infinitary formulas can be characterized in terms of infinitary equilibrium logic, verified that infinitary propositional fo ...
... defined the infinitary version of the logic of here-and-there, defined its nonmonotonic counterpart—the infinitary version of equilibrium logic, verified that stable models of infinitary formulas can be characterized in terms of infinitary equilibrium logic, verified that infinitary propositional fo ...
LOGICAL CONSEQUENCE AS TRUTH-PRESERVATION STEPHEN READ Abstract
... q is false. But I do not think that . . . the fact that it would be self-contradictory to assert that p is true but q is false is a sufficient condition for its being true that p implies q. ([16], p. 182) Lastly, take Gerhard Schurz’s programme of relevant deduction. In a recent paper, he describes ...
... q is false. But I do not think that . . . the fact that it would be self-contradictory to assert that p is true but q is false is a sufficient condition for its being true that p implies q. ([16], p. 182) Lastly, take Gerhard Schurz’s programme of relevant deduction. In a recent paper, he describes ...
On Rosser sentences and proof predicates
... predicate P r as the necessity operator in some suitable modal logic, and much work on modal fixed points was done in the seventies by C. Bernardi, D. de Jongh and G. Sambin. It was proven independently by the three that modal fixed points are unique, and de Jongh and Sambin also presented proofs ...
... predicate P r as the necessity operator in some suitable modal logic, and much work on modal fixed points was done in the seventies by C. Bernardi, D. de Jongh and G. Sambin. It was proven independently by the three that modal fixed points are unique, and de Jongh and Sambin also presented proofs ...
Properties of maximal cliques of a pair-wise compatibility graph for three nonmonotonic reasoning system
... Throughout this paper, we refer to maximal cliques as cliques. In the sequel, we consider graphs made of rules (either default theories or rules of normal logic programs and extended logic programs). We consider these concepts familiar and refer the reader to the basic sources on the subject [16] [1 ...
... Throughout this paper, we refer to maximal cliques as cliques. In the sequel, we consider graphs made of rules (either default theories or rules of normal logic programs and extended logic programs). We consider these concepts familiar and refer the reader to the basic sources on the subject [16] [1 ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
One-dimensional Fragment of First-order Logic
... logic. Decidability properties of several fragments of first-order logic have been investigated after the completion of the program concerning the classical decision problem. Currently perhaps the most important two frameworks studied in this context are the guarded fragment [1] and two-variable log ...
... logic. Decidability properties of several fragments of first-order logic have been investigated after the completion of the program concerning the classical decision problem. Currently perhaps the most important two frameworks studied in this context are the guarded fragment [1] and two-variable log ...
The Logic of Atomic Sentences
... since b = d, c is left of d by the Indiscernibility of Identicals. But we are also told that d is left of e, and consequently c is to the left of e, by the textbftransitivity of left of. Done. William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
... since b = d, c is left of d by the Indiscernibility of Identicals. But we are also told that d is left of e, and consequently c is to the left of e, by the textbftransitivity of left of. Done. William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
First-Order Loop Formulas for Normal Logic Programs
... gence (www.aaai.org). All rights reserved. ...
... gence (www.aaai.org). All rights reserved. ...
Notes on Modal Logic - Stanford University
... • Alethic Reading: 2ϕ means ‘ϕ is necessary’ and 3ϕ means ‘ϕ is possible’. • Deontic Reading: 2ϕ means ‘ϕ is obligatory’ and 3ϕ means ‘ϕ is permitted’. In this literature, typically ‘O’ is used instead of ‘2’ and ‘P ’ instead of ‘3’. • Epistemic Reading: 2ϕ means ‘ϕ is known’ and 3ϕ means ‘ϕ is cons ...
... • Alethic Reading: 2ϕ means ‘ϕ is necessary’ and 3ϕ means ‘ϕ is possible’. • Deontic Reading: 2ϕ means ‘ϕ is obligatory’ and 3ϕ means ‘ϕ is permitted’. In this literature, typically ‘O’ is used instead of ‘2’ and ‘P ’ instead of ‘3’. • Epistemic Reading: 2ϕ means ‘ϕ is known’ and 3ϕ means ‘ϕ is cons ...
A Generalization of St˚almarck`s Method
... Application of simple deductive rules: Stålmarck’s method applies a set of simple deductive rules after each split. In abstract-interpretation terms, the rules perform a semantic reduction [5] by means of a technique called local decreasing iterations [7]. “Intersecting” results: The step of combin ...
... Application of simple deductive rules: Stålmarck’s method applies a set of simple deductive rules after each split. In abstract-interpretation terms, the rules perform a semantic reduction [5] by means of a technique called local decreasing iterations [7]. “Intersecting” results: The step of combin ...
What Classical Connectives Mean
... realized inflexionally), there is some reason to describe the 'future tense' as partly modal. John Lyons, Introduc)on to Theore)cal Linguis)cs A A A ...
... realized inflexionally), there is some reason to describe the 'future tense' as partly modal. John Lyons, Introduc)on to Theore)cal Linguis)cs A A A ...
Using Modal Logics to Express and Check Global Graph Properties
... many efficient algorithmic methods to solve them. However, there is an important distinction between the two sides of this matter. In the “description” side, graphs provide a great level of generality, allowing for the description of very different problems in the same simple framework. But in the “ ...
... many efficient algorithmic methods to solve them. However, there is an important distinction between the two sides of this matter. In the “description” side, graphs provide a great level of generality, allowing for the description of very different problems in the same simple framework. But in the “ ...
Introduction to Logic
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...
GLukG logic and its application for non-monotonic reasoning
... Hilbert style proof systems There are many different approaches that have been used to specify the meaning of logic formulas or, in other words, to define logics. In Hilbert style proof systems, also known as axiomatic systems, a logic is specified by giving a set of axioms (which is usually assumed ...
... Hilbert style proof systems There are many different approaches that have been used to specify the meaning of logic formulas or, in other words, to define logics. In Hilbert style proof systems, also known as axiomatic systems, a logic is specified by giving a set of axioms (which is usually assumed ...
pdf
... generated by primitive propositions, that is, an agent is aware of a formula iff he is aware of all primitive propositions occurring in it, and agents know what they are aware of (so that each agent is aware of the same formulas in all worlds that he consider possible). As we pointed out in (Halpern ...
... generated by primitive propositions, that is, an agent is aware of a formula iff he is aware of all primitive propositions occurring in it, and agents know what they are aware of (so that each agent is aware of the same formulas in all worlds that he consider possible). As we pointed out in (Halpern ...
The Expressive Power of Modal Dependence Logic
... Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , ...
... Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , ...
preliminary version
... Intuitionism. Proof checkers based on type theory, like for instance Coq, work with intuitionistic logic, sometimes also called constructive logic. This is the logic of the natural deduction proof system discussed so far. The intuition is that truth in intuitionistic logic corresponds to the existen ...
... Intuitionism. Proof checkers based on type theory, like for instance Coq, work with intuitionistic logic, sometimes also called constructive logic. This is the logic of the natural deduction proof system discussed so far. The intuition is that truth in intuitionistic logic corresponds to the existen ...
pdf
... 1.1. Proof Systems Consider the boolean formula satisfiability problem, SAT. For formulas in SAT, there is always a short proof of satisfiability – a satisfying truth assignment – and therefore SAT is trivially in NP. However, for formulas not in SAT, it is not that clear what a proof of unsatisfiab ...
... 1.1. Proof Systems Consider the boolean formula satisfiability problem, SAT. For formulas in SAT, there is always a short proof of satisfiability – a satisfying truth assignment – and therefore SAT is trivially in NP. However, for formulas not in SAT, it is not that clear what a proof of unsatisfiab ...
PDF
... true, false, p, ¬ϕ, ϕ ∨ ψ, ϕ, 3ϕ, eϕ, or ϕU ψ, where p ∈ P , and ϕ and ψ are LTL formulas. The temporal operators (“always”), 3 (“eventually”), e(“next”), and U (“until”) enable convenient description of time-dependent events. For example, the LTL formula (request → 3grant) states that every req ...
... true, false, p, ¬ϕ, ϕ ∨ ψ, ϕ, 3ϕ, eϕ, or ϕU ψ, where p ∈ P , and ϕ and ψ are LTL formulas. The temporal operators (“always”), 3 (“eventually”), e(“next”), and U (“until”) enable convenient description of time-dependent events. For example, the LTL formula (request → 3grant) states that every req ...
Modal logic and the approximation induction principle
... Hennessy–Milner logic [14] is a modal logic for specifying properties of states in a labelled transition system (LTS). Rob van Glabbeek [11] uses this logic to characterize a wide range of process semantics in terms of observations. That is, a process semantics is captured by means of a sublogic of ...
... Hennessy–Milner logic [14] is a modal logic for specifying properties of states in a labelled transition system (LTS). Rob van Glabbeek [11] uses this logic to characterize a wide range of process semantics in terms of observations. That is, a process semantics is captured by means of a sublogic of ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
Completeness in modal logic - Lund University Publications
... That essay was focused on the philosophy of semantics for modal logics, with special attention to completeness results. The purpose of the essay was to exhibit a negative trend in modal logic regarded as a philosophical discipline; the enterprise of completeness proving has become largely “l’art pou ...
... That essay was focused on the philosophy of semantics for modal logics, with special attention to completeness results. The purpose of the essay was to exhibit a negative trend in modal logic regarded as a philosophical discipline; the enterprise of completeness proving has become largely “l’art pou ...
Intuitionistic Type Theory
... (⊥, ⊃, &, ∨, ∀, ∃) and hold to be true are propositions. When we hold a proposition to be true, we make a judgement: ...
... (⊥, ⊃, &, ∨, ∀, ∃) and hold to be true are propositions. When we hold a proposition to be true, we make a judgement: ...
Knowledge Representation and Classical Logic
... clear that F is equivalent to G if and only if F ↔ G is a tautology. A set Γ of formulas is satisfiable if there exists an interpretation satisfying all formulas in Γ. We say that Γ entails a formula F (symbolically, Γ |= F ) if every interpretation satisfying Γ satisfies F .2 To represent knowledge ...
... clear that F is equivalent to G if and only if F ↔ G is a tautology. A set Γ of formulas is satisfiable if there exists an interpretation satisfying all formulas in Γ. We say that Γ entails a formula F (symbolically, Γ |= F ) if every interpretation satisfying Γ satisfies F .2 To represent knowledge ...