Consequence Operators for Defeasible - SeDiCI
... proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other con°icting arguments. In this context, defeasible consequence relationships for modeling argument and warrant as well as their logical properties have gained particular attention. The study of logical pr ...
... proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other con°icting arguments. In this context, defeasible consequence relationships for modeling argument and warrant as well as their logical properties have gained particular attention. The study of logical pr ...
Combining Paraconsistent Logic with Argumentation
... arguments (if not themselves defeated) cannot be labelled in or out, their targets can also not be labelled in or out. But then neither A2 nor B2 can be labelled in or out, since they are both indirectly defeated by the self-defeating argument. Therefore neither A2 nor B2 will be in any preferred e ...
... arguments (if not themselves defeated) cannot be labelled in or out, their targets can also not be labelled in or out. But then neither A2 nor B2 can be labelled in or out, since they are both indirectly defeated by the self-defeating argument. Therefore neither A2 nor B2 will be in any preferred e ...
The Foundations
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
The Foundations
... is true ? => The proposition: “It_is_raining” is true if the meaning (or fact) that the proposition is intended to represent occurs (happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now (the current situation), the statement “It_is_r ...
... is true ? => The proposition: “It_is_raining” is true if the meaning (or fact) that the proposition is intended to represent occurs (happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now (the current situation), the statement “It_is_r ...
Modal Logic - Web Services Overview
... 1. So we can use only one of the two operators, for instance “necessary” 2. But it is more convenient to use two operators. ...
... 1. So we can use only one of the two operators, for instance “necessary” 2. But it is more convenient to use two operators. ...
full text (.pdf)
... models in which set expressions are interpreted as sets of ground terms, as well as nonstandard models in which set expressions are interpreted as sets of states of term automata KPS92]. In this paper we propose a Gentzen-style axiomatization involving sequents of the form ` , where and are nit ...
... models in which set expressions are interpreted as sets of ground terms, as well as nonstandard models in which set expressions are interpreted as sets of states of term automata KPS92]. In this paper we propose a Gentzen-style axiomatization involving sequents of the form ` , where and are nit ...
The Foundations
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
self-reference in arithmetic i - Utrecht University Repository
... has been used in different ways and may be misleading. Presumably selfpredication cannot so easily be understood in a deviant way and therefore would be preferable. However, since the term self-reference has become common parlance, it will be used here and our observations in this paper are explicit ...
... has been used in different ways and may be misleading. Presumably selfpredication cannot so easily be understood in a deviant way and therefore would be preferable. However, since the term self-reference has become common parlance, it will be used here and our observations in this paper are explicit ...
CS243: Discrete Structures Mathematical Proof Techniques
... This makes no difference from a logical point of view, but sometimes the contrapositive is easier to show by direct proof than the original ...
... This makes no difference from a logical point of view, but sometimes the contrapositive is easier to show by direct proof than the original ...
Introduction to first order logic for knowledge representation
... are used to indicate the basic (atomic) components of the (part of the) world the logic is supposed to describe. The alphabet is composed of two subsets: the logical symbols and the non logical symbols. Examples of such atomic objects are, individuals, functions, operators, truth-values, proposition ...
... are used to indicate the basic (atomic) components of the (part of the) world the logic is supposed to describe. The alphabet is composed of two subsets: the logical symbols and the non logical symbols. Examples of such atomic objects are, individuals, functions, operators, truth-values, proposition ...
The Foundations
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
... Compound propositions: (p q) r Equivalences: pq (p q) Proving equivalences using: Truth tables. Symbolic derivations. p q r … ...
Automated Deduction Looking Ahead
... decision procedure when provided a fixed propositional formula but is also a first-order logic proof procedure whenever larger propositional formulas are formed in a standard way from the given first-order formula. Although the later resolution proof method formalized a generally better way of relat ...
... decision procedure when provided a fixed propositional formula but is also a first-order logic proof procedure whenever larger propositional formulas are formed in a standard way from the given first-order formula. Although the later resolution proof method formalized a generally better way of relat ...
(pdf)
... undecidable, that is it is neither provable nor refutable. For now, we stick to an informal discussion of these concepts, but we will give precise formulations in the next section of this paper. The philosophical signi cance of this theorem is that it establishes the mutual exclusivity of completene ...
... undecidable, that is it is neither provable nor refutable. For now, we stick to an informal discussion of these concepts, but we will give precise formulations in the next section of this paper. The philosophical signi cance of this theorem is that it establishes the mutual exclusivity of completene ...
MATH20302 Propositional Logic
... bind more closely than → and ↔ (at least those are my conventions, but they are not universal). Therefore ¬p ∧ q → r means ((¬p) ∧ q) → r rather than ¬(p ∧ q) → r or (¬p) ∧ (q → r) or ¬(p ∧ (q → r)) (at least it does to me; if in doubt, put in more parentheses). You will recall that in order to prov ...
... bind more closely than → and ↔ (at least those are my conventions, but they are not universal). Therefore ¬p ∧ q → r means ((¬p) ∧ q) → r rather than ¬(p ∧ q) → r or (¬p) ∧ (q → r) or ¬(p ∧ (q → r)) (at least it does to me; if in doubt, put in more parentheses). You will recall that in order to prov ...
SLD-Resolution And Logic Programming (PROLOG)
... restricted to propositions, S → has a G! -proof T ! in which all axioms are atomic. Using lemma 4.2.2, S → has a G! -proof T !! in which all axioms are atomic, and in which all applications of the ∨ : lef t rule precede all applications of the ¬ : lef t rule. The tree obtained from T !! by retaining ...
... restricted to propositions, S → has a G! -proof T ! in which all axioms are atomic. Using lemma 4.2.2, S → has a G! -proof T !! in which all axioms are atomic, and in which all applications of the ∨ : lef t rule precede all applications of the ¬ : lef t rule. The tree obtained from T !! by retaining ...
Pebble weighted automata and transitive - LSV
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
Belief Revision in non
... the following components: i) a sound and complete classical logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined ...
... the following components: i) a sound and complete classical logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined ...
Introduction to Mathematical Logic lecture notes
... Lemma 1.2.13. Let Γ be a finitely satisfiable set of formulae and ϕ a formula. Then at least one of Γ ∪ {ϕ} or Γ ∪ {¬ϕ} is finitely satisfiable. Proof. Assume for a contradiction that neither is. Then there are finite subsets Γ0 , Γ1 ⊆ Γ such that neither Γ0 ∪ {ϕ} nor Γ1 ∪ {¬ϕ} are satisfiable. But Γ0 ...
... Lemma 1.2.13. Let Γ be a finitely satisfiable set of formulae and ϕ a formula. Then at least one of Γ ∪ {ϕ} or Γ ∪ {¬ϕ} is finitely satisfiable. Proof. Assume for a contradiction that neither is. Then there are finite subsets Γ0 , Γ1 ⊆ Γ such that neither Γ0 ∪ {ϕ} nor Γ1 ∪ {¬ϕ} are satisfiable. But Γ0 ...
A Deduction Method Complete for Refutation and Finite Satis ability
... from programs, e.g. loop invariants. Often enough, program drafts do not ful ll their speci cations. Model generators can be applied to (a logic representation of) the programs to generate \samples", or \cases" in which a requirement is violated. These samples can then be used for correcting the pro ...
... from programs, e.g. loop invariants. Often enough, program drafts do not ful ll their speci cations. Model generators can be applied to (a logic representation of) the programs to generate \samples", or \cases" in which a requirement is violated. These samples can then be used for correcting the pro ...
A Hennessy-Milner Property for Many
... mostly on issues of axiomatization, decidability, and complexity. Other topics from the rich theory of modal logics, such as first-order correspondence theory, canonical models, etc. have not as yet received much attention. In particular, the general question of the expressivity of many-valued modal ...
... mostly on issues of axiomatization, decidability, and complexity. Other topics from the rich theory of modal logics, such as first-order correspondence theory, canonical models, etc. have not as yet received much attention. In particular, the general question of the expressivity of many-valued modal ...
Logic and Sets
... Given positive integers m and n, we say that m is a factor of n provided n = mq for some positive integer q. In particular, n is a factor of itself, since n = n · 1. If m is a factor of n and m < n, then m is called a proper factor of n. For example, the proper factors of 6 are 1, 2, and 3, and the ...
... Given positive integers m and n, we say that m is a factor of n provided n = mq for some positive integer q. In particular, n is a factor of itself, since n = n · 1. If m is a factor of n and m < n, then m is called a proper factor of n. For example, the proper factors of 6 are 1, 2, and 3, and the ...
DIPLOMAMUNKA
... According to Chaitin (1995), Gödel once told him “it doesnt matter which paradox you use [to prove the first incompleteness theorem]”. However, there is no proof that for every (logical) paradox there is a corresponding undecidable sentence in Peano arithmetic. Therefore it is worth to investigate ...
... According to Chaitin (1995), Gödel once told him “it doesnt matter which paradox you use [to prove the first incompleteness theorem]”. However, there is no proof that for every (logical) paradox there is a corresponding undecidable sentence in Peano arithmetic. Therefore it is worth to investigate ...
CS389L: Automated Logical Reasoning Lecture 1
... Formulas F1 and F2 are equivalent (written F1 ⇔ F2 ) iff for all interpretations I , I |= F1 ↔ F2 F1 ⇔ F2 iff F1 ↔ F2 is valid ...
... Formulas F1 and F2 are equivalent (written F1 ⇔ F2 ) iff for all interpretations I , I |= F1 ↔ F2 F1 ⇔ F2 iff F1 ↔ F2 is valid ...
A Tableau Calculus for Minimal Modal Model Generation
... attention for modal logics with non-monotonic operators and non-monotonic semantics, where the aim is the minimization of certain predicates (for example [6,7]). As the common modal logics can be translated into first-order logic [14], classical approaches for minimal model generation can be used to ...
... attention for modal logics with non-monotonic operators and non-monotonic semantics, where the aim is the minimization of certain predicates (for example [6,7]). As the common modal logics can be translated into first-order logic [14], classical approaches for minimal model generation can be used to ...
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 ...