Uniform satisfiability in PSPACE for local temporal logics over
... PSPACE-complete and LTL over words is a special case of most local temporal logics over traces. Several local temporal logics were introduced [18, 1, 8, 3] and each time the complexity was proved to be in PSPACE or EXPTIME. Whenever a new local temporal logic was introduced, a new proof of the compl ...
... PSPACE-complete and LTL over words is a special case of most local temporal logics over traces. Several local temporal logics were introduced [18, 1, 8, 3] and each time the complexity was proved to be in PSPACE or EXPTIME. Whenever a new local temporal logic was introduced, a new proof of the compl ...
A Computationally-Discovered Simplification of the Ontological
... Anselm’s ontological argument has come in for criticism ever since it was first proposed. But we think that the focus on finding flaws in the argument may have hindered progress in logically representing the argument in its most elegant form. We hope to show that computational techniques offer a new ...
... Anselm’s ontological argument has come in for criticism ever since it was first proposed. But we think that the focus on finding flaws in the argument may have hindered progress in logically representing the argument in its most elegant form. We hope to show that computational techniques offer a new ...
A Computationally-Discovered Simplification of the Ontological
... Anselm’s ontological argument has come in for criticism ever since it was first proposed. But we think that the focus on finding flaws in the argument may have hindered progress in logically representing the argument in its most elegant form. We hope to show that computational techniques offer a new ...
... Anselm’s ontological argument has come in for criticism ever since it was first proposed. But we think that the focus on finding flaws in the argument may have hindered progress in logically representing the argument in its most elegant form. We hope to show that computational techniques offer a new ...
Provability as a Modal Operator with the models of PA as the Worlds
... Theorem 3: MB , A (ψ → ψ) → ψ for all worlds A and arbitrary modal formulae ψ. Proof: B is Löbian so all three of Löb’s conditions hold. Furthermore, the diagonalization lemma applies to any formula B of first order arithmetic, so we can construct γ such that PA ⊢ γ ↔ [Bγ → ϕ]. These are all th ...
... Theorem 3: MB , A (ψ → ψ) → ψ for all worlds A and arbitrary modal formulae ψ. Proof: B is Löbian so all three of Löb’s conditions hold. Furthermore, the diagonalization lemma applies to any formula B of first order arithmetic, so we can construct γ such that PA ⊢ γ ↔ [Bγ → ϕ]. These are all th ...
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 ...
Equivalence for the G3'-stable models semantics
... they have the same G03 -stable models. The notion of strongly equivalent logic programs is interesting since, given two sets of rules that are strongly equivalent, one of them can be replaced by the other one in any logic program without changing the declarative semantics of the program. This replac ...
... they have the same G03 -stable models. The notion of strongly equivalent logic programs is interesting since, given two sets of rules that are strongly equivalent, one of them can be replaced by the other one in any logic program without changing the declarative semantics of the program. This replac ...
An Institution-Independent Generalization of Tarski`s Elementary
... The notion of elementary embedding is an important one in classical first-order model theory [4]. Elementary chains (i.e., chains of elementary embeddings) are known to be a fundamental proof tool for results regarding preservation of satisfaction, axiomatizability, Robinson consistency, Craig inter ...
... The notion of elementary embedding is an important one in classical first-order model theory [4]. Elementary chains (i.e., chains of elementary embeddings) are known to be a fundamental proof tool for results regarding preservation of satisfaction, axiomatizability, Robinson consistency, Craig inter ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
... of minimizing knowledge in terms of the world knowledge of the agent gives rise to several interesting features from the viewpoint of knowledge representation. In particular, the restriction to grounded assumptions can be regarded as a a refinement of the introspection capabilities provided by McDer ...
... of minimizing knowledge in terms of the world knowledge of the agent gives rise to several interesting features from the viewpoint of knowledge representation. In particular, the restriction to grounded assumptions can be regarded as a a refinement of the introspection capabilities provided by McDer ...
Default Logic (Reiter) - Department of Computing
... classical consequence Th, and closed under the default rules D that are applicable given E. It remains to define what ‘closed under the default rules D that are applicable given E’ means. A formal definition follows presently. ...
... classical consequence Th, and closed under the default rules D that are applicable given E. It remains to define what ‘closed under the default rules D that are applicable given E’ means. A formal definition follows presently. ...
Understanding SPKI/SDSI Using First-Order Logic
... In the present paper, we show that standard first-order logic (FOL) provides a natural semantics for SPKI/SDSI and that the FOL semantics has several advantages over previous approaches. In our study of the SDSI naming portion of SPKI/SDSI (Section 2 of this paper), we present a FOL semantics based ...
... In the present paper, we show that standard first-order logic (FOL) provides a natural semantics for SPKI/SDSI and that the FOL semantics has several advantages over previous approaches. In our study of the SDSI naming portion of SPKI/SDSI (Section 2 of this paper), we present a FOL semantics based ...
1Propositional Logic - Princeton University Press
... We list the logical connectives with their English labels. (The negation symbol doesn’t connect anything; it only has one argument. However, for convenience we ignore that detail and call all the listed logical symbols “connectives.”) ...
... We list the logical connectives with their English labels. (The negation symbol doesn’t connect anything; it only has one argument. However, for convenience we ignore that detail and call all the listed logical symbols “connectives.”) ...
A Logical Foundation for Session
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
Intuitionistic completeness part I
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
Proof analysis beyond geometric theories: from rule systems to
... has brought a wealth of applications to the proof theory of non-classican logics, including provability logic (Negri 2005), substructural logic (Negri 2008), intermediate logics (Dyckhoff and Negri 2012), conditional logics (Olivetti et al. 2007), description logics (de Paiva et al. 2011), systems f ...
... has brought a wealth of applications to the proof theory of non-classican logics, including provability logic (Negri 2005), substructural logic (Negri 2008), intermediate logics (Dyckhoff and Negri 2012), conditional logics (Olivetti et al. 2007), description logics (de Paiva et al. 2011), systems f ...
relevance logic - Consequently.org
... Before turning to matters of logical substance, let us first introduce a framework for grammar and nomenclature that is helpful in understanding the ways that writers on relevance logic often express themselves. We draw heavily on the ‘Grammatical Propaedeutic’ appendix of [Anderson and Belnap, 1975 ...
... Before turning to matters of logical substance, let us first introduce a framework for grammar and nomenclature that is helpful in understanding the ways that writers on relevance logic often express themselves. We draw heavily on the ‘Grammatical Propaedeutic’ appendix of [Anderson and Belnap, 1975 ...
Combining Paraconsistent Logic with Argumentation
... of the argumentation system, while the other is to derive the strict inference rules from a weaker logic than classical logic. The first approach is taken by Wu [6], who for the ASPIC+ framework [7,8] requires that for each argument the set of conclusions of all its subarguments are classically cons ...
... of the argumentation system, while the other is to derive the strict inference rules from a weaker logic than classical logic. The first approach is taken by Wu [6], who for the ASPIC+ framework [7,8] requires that for each argument the set of conclusions of all its subarguments are classically cons ...
Towards an Epistemic Logic of Grounded Belief
... an ideal agent cannot posses knowledge of falsity. For any situation it seems strange to say that one may know a falsehood in that situation. The principle that in any situation if one knows some proposition φ, then φ is true goes back to at least Plato (1999a) and possibly Parmenides. However, some ...
... an ideal agent cannot posses knowledge of falsity. For any situation it seems strange to say that one may know a falsehood in that situation. The principle that in any situation if one knows some proposition φ, then φ is true goes back to at least Plato (1999a) and possibly Parmenides. However, some ...
PPT - UBC Department of CPSC Undergraduates
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
Section 1: Propositional Logic
... of the equivalent statement forms ∼q ⇒ ∼p or p ⇒ q, whichever is most convenient for the discussion at hand. • if and only if: The biconditional, p ⇔ q is sometimes stated as “p if and only if q” and written “p iff q”. • sufficient: The expression, “p is sufficient for q”(or “p is a sufficient condi ...
... of the equivalent statement forms ∼q ⇒ ∼p or p ⇒ q, whichever is most convenient for the discussion at hand. • if and only if: The biconditional, p ⇔ q is sometimes stated as “p if and only if q” and written “p iff q”. • sufficient: The expression, “p is sufficient for q”(or “p is a sufficient condi ...
The Journal of Functional and Logic Programming The MIT Press
... scheme, consider a CLP(X1 , . . . , Xn ) solver with two constraint domains, X1 and X2 and respective solvers S1 and S2 . Suppose that S2 is a solver for systems of equations and disequations over the real numbers, while S1 is a simple scheduler which, given a number of activities classified by type ...
... scheme, consider a CLP(X1 , . . . , Xn ) solver with two constraint domains, X1 and X2 and respective solvers S1 and S2 . Suppose that S2 is a solver for systems of equations and disequations over the real numbers, while S1 is a simple scheduler which, given a number of activities classified by type ...
A System of Interaction and Structure
... atomic cut, but all the rules in the decomposition of cut can be shown admissible. An advantage is that one can have a wide range of equivalent systems (one for each combination of admissible rules), with varying degrees of expressiveness in proof construction. All the admissible rules are in fact i ...
... atomic cut, but all the rules in the decomposition of cut can be shown admissible. An advantage is that one can have a wide range of equivalent systems (one for each combination of admissible rules), with varying degrees of expressiveness in proof construction. All the admissible rules are in fact i ...
Introduction to Logic
... other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only lies at its origin, ca. 500 BC, but has been the main force motivating its development since that time until the last century. There was a medieval tradition according to which the Greek philos ...
... other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only lies at its origin, ca. 500 BC, but has been the main force motivating its development since that time until the last century. There was a medieval tradition according to which the Greek philos ...
The Pure Calculus of Entailment Author(s): Alan Ross Anderson and
... part HI of the intuitionist propositional calculus, especially from the point of view of Fitch 1952. In sections II and III we argue that HI is unsatisfactory as a formalization of entailment on two distinct counts, and in section IV we offer a system EI (derived from Ackermann 1956) intended to cap ...
... part HI of the intuitionist propositional calculus, especially from the point of view of Fitch 1952. In sections II and III we argue that HI is unsatisfactory as a formalization of entailment on two distinct counts, and in section IV we offer a system EI (derived from Ackermann 1956) intended to cap ...
tbmk5ictk6
... two examples of valid arguments; one of them was sound and the other was not. Since both examples were valid, the one with true premises was the one that was sound. We also saw two examples of invalid arguments. Both of those are unsound simply because they are invalid. Sound arguments have to be v ...
... two examples of valid arguments; one of them was sound and the other was not. Since both examples were valid, the one with true premises was the one that was sound. We also saw two examples of invalid arguments. Both of those are unsound simply because they are invalid. Sound arguments have to be v ...
Logic in Nonmonotonic Reasoning
... knowledge bases, when such hierarchies have been allowed to have exceptions. The theory of reasoning in such taxonomies has been called nonmonotonic inheritance (see [Horty, 1994] for an overview). The guiding principle in resolving potential conflicts in such hierarchies was a specificity principl ...
... knowledge bases, when such hierarchies have been allowed to have exceptions. The theory of reasoning in such taxonomies has been called nonmonotonic inheritance (see [Horty, 1994] for an overview). The guiding principle in resolving potential conflicts in such hierarchies was a specificity principl ...
Jesús Mosterín
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Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.