An argumentation framework in default logic
... conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real life people do not always have sufficient information to make a safe step towards the conclusion; instead, they often jump to conclusions by applying general, defeas ...
... conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real life people do not always have sufficient information to make a safe step towards the conclusion; instead, they often jump to conclusions by applying general, defeas ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... proposition “a→b” from the KB. Alternatively, one could ignore the revision and keep the KB as is. Finally, several other options can be imagined, such as replacing a proposition of the KB with another, or dropping both propositions etc. All the above approaches succeed in accommodating the revision ...
... proposition “a→b” from the KB. Alternatively, one could ignore the revision and keep the KB as is. Finally, several other options can be imagined, such as replacing a proposition of the KB with another, or dropping both propositions etc. All the above approaches succeed in accommodating the revision ...
Intuitionistic Logic - Institute for Logic, Language and Computation
... • ¬ ¬∀xφ(x) → ∀x¬ ¬φ(x) (but not its converse). The BHK-interpretation was independently given by Kolmogorov and Heyting, with Kolmogorov’s formulation in terms of the solution of problems rather than in terms of executing proofs. Of course, both extracted the idea from Brouwer’s work. In any case, ...
... • ¬ ¬∀xφ(x) → ∀x¬ ¬φ(x) (but not its converse). The BHK-interpretation was independently given by Kolmogorov and Heyting, with Kolmogorov’s formulation in terms of the solution of problems rather than in terms of executing proofs. Of course, both extracted the idea from Brouwer’s work. In any case, ...
Relevant and Substructural Logics
... premises to a conclusion, but rather relate lists, or other forms of structured collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define ...
... premises to a conclusion, but rather relate lists, or other forms of structured collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define ...
Carnap and Quine on the analytic-synthetic - Philsci
... frameworks have immediate repercussions for the analyticity of the non-factual statements in these frameworks. It will transpire that the class of statements Quine would accept as analytic is much more restricted than what Carnap would allow. Nevertheless, Quine’s most convincing argument against Ca ...
... frameworks have immediate repercussions for the analyticity of the non-factual statements in these frameworks. It will transpire that the class of statements Quine would accept as analytic is much more restricted than what Carnap would allow. Nevertheless, Quine’s most convincing argument against Ca ...
Formal Theories of Truth INTRODUCTION
... theorems is itself already a proof of the general principle; this principle represents, so to speak, an ‘infinite logical product’ of those special theorems. But this does not at all mean that we can actually derive the principle of contradiction from the axioms or theorems mentioned by means of the ...
... theorems is itself already a proof of the general principle; this principle represents, so to speak, an ‘infinite logical product’ of those special theorems. But this does not at all mean that we can actually derive the principle of contradiction from the axioms or theorems mentioned by means of the ...
![Propositions as [Types] - Research Showcase @ CMU](http://s1.studyres.com/store/data/005730189_1-e85fa7d3c7cfa08d9a3b8e96a27d7888-300x300.png)
Propositions as [Types] - Research Showcase @ CMU
... types of Maietti [Mai98], in a suitable setting. Palmgren [Pal01] formulated a BHK interpretation of intuitionistic logic and used image factorizations, which are used in the semantics of our bracket types, to relate the BHK interpretation to the standard category-theoretic interpretation of proposi ...
... types of Maietti [Mai98], in a suitable setting. Palmgren [Pal01] formulated a BHK interpretation of intuitionistic logic and used image factorizations, which are used in the semantics of our bracket types, to relate the BHK interpretation to the standard category-theoretic interpretation of proposi ...
Equality in the Presence of Apartness: An Application of Structural
... may require that a and b are computed to infinite precision. If a and b are positively distinct, instead, a finite computation is sufficient. Thus, Brouwer introduced the notion of apartness as a positive, intuitionistic basic concept. He also introduced special notations and terminology for the new int ...
... may require that a and b are computed to infinite precision. If a and b are positively distinct, instead, a finite computation is sufficient. Thus, Brouwer introduced the notion of apartness as a positive, intuitionistic basic concept. He also introduced special notations and terminology for the new int ...
Notes on Modal Logic - Stanford University
... The modal invariance Lemma (Lemma 3.7) can be used to prove what can and cannot be expressed in the basic modal language. Fact 3.9 Let M = hW, R, V i be a relational structure. The universal operator is a unary operator Aϕ defined as follows: M, w |= Aϕ iff for all v ∈ W , M, v |= ϕ The universal o ...
... The modal invariance Lemma (Lemma 3.7) can be used to prove what can and cannot be expressed in the basic modal language. Fact 3.9 Let M = hW, R, V i be a relational structure. The universal operator is a unary operator Aϕ defined as follows: M, w |= Aϕ iff for all v ∈ W , M, v |= ϕ The universal o ...
Finite satisfiability for guarded fixpoint logic
... Main Theorem 1. It is decidable whether or not a given guarded fixpoint sentence is finitely satisfiable. The problem is 2ExpTimecomplete in general, and ExpTime-complete for formulas of bounded width. As noted above the stated hardness results already hold for the guarded fragment [5]. The proof of th ...
... Main Theorem 1. It is decidable whether or not a given guarded fixpoint sentence is finitely satisfiable. The problem is 2ExpTimecomplete in general, and ExpTime-complete for formulas of bounded width. As noted above the stated hardness results already hold for the guarded fragment [5]. The proof of th ...
CS389L: Automated Logical Reasoning Lecture 1
... iff I 6|= F iff I |= F1 and I |= F2 iff I |= F1 or I |= F2 iff, I 6|= F1 or I |= F2 iff, I |= F1 and I |= F2 or I 6|= F1 and I 6|= F2 ...
... iff I 6|= F iff I |= F1 and I |= F2 iff I |= F1 or I |= F2 iff, I 6|= F1 or I |= F2 iff, I |= F1 and I |= F2 or I 6|= F1 and I 6|= F2 ...
Modal Languages and Bounded Fragments of Predicate Logic
... These are needed to get the exact correspondence with closed semantic tableaus right. Note that the classical structural rule of Contraction is redundant for the completeness proof. (It deduces Σ, A ⇒ ∆ from Σ, A, A ⇒ ∆.) In classical tableaus or sequent proofs for predicate logic, this rule ensures ...
... These are needed to get the exact correspondence with closed semantic tableaus right. Note that the classical structural rule of Contraction is redundant for the completeness proof. (It deduces Σ, A ⇒ ∆ from Σ, A, A ⇒ ∆.) In classical tableaus or sequent proofs for predicate logic, this rule ensures ...
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 ...
Chapter X: Computational Complexity of Propositional Fuzzy Logics
... some complexity class), the situation is analogous to the classical case: satisfiability is NP-complete, while tautologousness and consequence (hence, theoremhood and provability) are coNP-complete. One might ask why consequence relation comes out no more difficult than tautologousness. This chapter ...
... some complexity class), the situation is analogous to the classical case: satisfiability is NP-complete, while tautologousness and consequence (hence, theoremhood and provability) are coNP-complete. One might ask why consequence relation comes out no more difficult than tautologousness. This chapter ...
Kripke Semantics for Basic Sequent Systems
... This paper is a continuation of an on-going project aiming to get a unified semantic theory and understanding of analytic Gentzen-type systems and the phenomenon of strong cut-admissibility in them. In particular: we seek for general effective criteria that can tell in advance whether a given system ...
... This paper is a continuation of an on-going project aiming to get a unified semantic theory and understanding of analytic Gentzen-type systems and the phenomenon of strong cut-admissibility in them. In particular: we seek for general effective criteria that can tell in advance whether a given system ...
Complete Sequent Calculi for Induction and Infinite Descent
... which case Γω ⊢ ∆ω is the “limit union” of the sequents along this branch. • Either way, we show Γω ⊢ ∆ω is not provable (this uses the trace condition). • Thus we can use Γω ⊢ ∆ω to construct a syntactic counter-model (the inductive predicate case also uses the ...
... which case Γω ⊢ ∆ω is the “limit union” of the sequents along this branch. • Either way, we show Γω ⊢ ∆ω is not provable (this uses the trace condition). • Thus we can use Γω ⊢ ∆ω to construct a syntactic counter-model (the inductive predicate case also uses the ...
Document
... Conjunction is a binary operator in that it operates on two propositions when creating compound proposition. On the other hand, negation is a unary operator (the only non-trivial one possible). ...
... Conjunction is a binary operator in that it operates on two propositions when creating compound proposition. On the other hand, negation is a unary operator (the only non-trivial one possible). ...
On modal logics of group belief
... an institution is grounded on the (individual and collective) acceptances of its members, and its dynamics depends on the dynamics of these acceptances. On this aspect we agree with Mantzavinos et al. [47], when the authors say that (p. 77): ‘only because institutions are anchored in peoples minds d ...
... an institution is grounded on the (individual and collective) acceptances of its members, and its dynamics depends on the dynamics of these acceptances. On this aspect we agree with Mantzavinos et al. [47], when the authors say that (p. 77): ‘only because institutions are anchored in peoples minds d ...
Proof Theory of Finite-valued Logics
... with outermost logical symbol 2n . (3) If A is a formula (semi-formula) not containing the bound variable x, a is a free variable and Q is a quantifier, then (Qx)A(x), where A(x) is obtained from A by replacing a by x at every occurrence of a in A, is a formula (semi-formula). Its outermost logical ...
... with outermost logical symbol 2n . (3) If A is a formula (semi-formula) not containing the bound variable x, a is a free variable and Q is a quantifier, then (Qx)A(x), where A(x) is obtained from A by replacing a by x at every occurrence of a in A, is a formula (semi-formula). Its outermost logical ...
A Contraction-free and Cut-free Sequent Calculus for
... From the point of view of Hilbert systems, propositional dynamic logic is well-defined. Indeed, there are several equivalent axiomatisations of P DL (see for example [4, 7]), each of which is obtained by adding to classical propositional logic: (i) the distribution axiom schema, that now has the form ...
... From the point of view of Hilbert systems, propositional dynamic logic is well-defined. Indeed, there are several equivalent axiomatisations of P DL (see for example [4, 7]), each of which is obtained by adding to classical propositional logic: (i) the distribution axiom schema, that now has the form ...
notes
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
Peano`s Arithmetic
... back to the publisher with corrections and his own suggestions for improvement. He even asked for permission to publish Genocchi’s lectures. After fixing some errors and adding his own comments to the collection, he only listed himself as an editor [2]. In 1884 Peano became a professor at the univer ...
... back to the publisher with corrections and his own suggestions for improvement. He even asked for permission to publish Genocchi’s lectures. After fixing some errors and adding his own comments to the collection, he only listed himself as an editor [2]. In 1884 Peano became a professor at the univer ...
Combining Paraconsistent Logic with Argumentation
... rule’s antecedents are accepted, then if the rule is strict, its consequent must be accepted no matter what, while if the rule is defeasible, its consequent must be accepted if there are no good reasons not to accept it. Arguments can be attacked on their (ordinary) premises and on their application ...
... rule’s antecedents are accepted, then if the rule is strict, its consequent must be accepted no matter what, while if the rule is defeasible, its consequent must be accepted if there are no good reasons not to accept it. Arguments can be attacked on their (ordinary) premises and on their application ...
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 ...