A modal perspective on monadic second
... graphs. This is a response to an open problem posed in [4] and [8]. We also provide modal characterizations of the expressive power of Monadic Second-Order Logic (MSO) and address a number of points that should promote the potential advantages of viewing MSO and its fragments from the modal perspect ...
... graphs. This is a response to an open problem posed in [4] and [8]. We also provide modal characterizations of the expressive power of Monadic Second-Order Logic (MSO) and address a number of points that should promote the potential advantages of viewing MSO and its fragments from the modal perspect ...
Deciding Intuitionistic Propositional Logic via Translation into
... “root”-world and A is a conjunction of axiom formulas encoding the logic-specific properties of R (e.g. reflexivity, transitivity, symmetry, etc.). This technique has two major disadvantages: On the one hand the classical theorem prover has to reason about the semantics of the given logic over and o ...
... “root”-world and A is a conjunction of axiom formulas encoding the logic-specific properties of R (e.g. reflexivity, transitivity, symmetry, etc.). This technique has two major disadvantages: On the one hand the classical theorem prover has to reason about the semantics of the given logic over and o ...
Quantitative Temporal Logics: PSPACE and below - FB3
... bers coded in unary, is PS PACE-complete without FVA [5]. In the technical report accompanying this paper, we show that our proof method can be used for other logics as well. For instance, metric extensions of (discrete-time) LTL and the branching time logic CTL are shown to be in PS PACE and E XP ...
... bers coded in unary, is PS PACE-complete without FVA [5]. In the technical report accompanying this paper, we show that our proof method can be used for other logics as well. For instance, metric extensions of (discrete-time) LTL and the branching time logic CTL are shown to be in PS PACE and E XP ...
Mathematical Logic. An Introduction
... A closer analysis of circularity in logic leads to the famous incompleteness theorems of Gödel’s: Theorem. Formal theories which are strong enough to “formalize themselves” are not complete, i.e., there are statements such that neither it nor its negation can be proved in that theory. Moreover such ...
... A closer analysis of circularity in logic leads to the famous incompleteness theorems of Gödel’s: Theorem. Formal theories which are strong enough to “formalize themselves” are not complete, i.e., there are statements such that neither it nor its negation can be proved in that theory. Moreover such ...
Introduction to Logic
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
Notes on Classical Propositional Logic
... means). In a course discussing a wide variety of logics, this is a natural place to start. Many different proof procedures have been developed for it: axiom systems, tree (tableau) systems, sequent calculi, natural deduction, resolution, and more. Some of these carry over to some other logics, and s ...
... means). In a course discussing a wide variety of logics, this is a natural place to start. Many different proof procedures have been developed for it: axiom systems, tree (tableau) systems, sequent calculi, natural deduction, resolution, and more. Some of these carry over to some other logics, and s ...
Logical Argument
... (see formal logic). Johnson and Blair (1987) define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse." Opinion pieces of newspapers ...
... (see formal logic). Johnson and Blair (1987) define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse." Opinion pieces of newspapers ...
Proof analysis beyond geometric theories: from rule systems to
... certain statements and thus obtaining proofs of independence; further on, they can be used for establishing conservativity of extensions, faithfulness of embeddings between logical systems, and in general for results that involve the simultaneous analysis of derivability in different theories. The s ...
... certain statements and thus obtaining proofs of independence; further on, they can be used for establishing conservativity of extensions, faithfulness of embeddings between logical systems, and in general for results that involve the simultaneous analysis of derivability in different theories. The s ...
From Answer Set Logic Programming to Circumscription via Logic of
... Answer Set Programming (ASP) is a new paradigm of constraint-based programming based on logic programming with answer set semantics 17,9,13]. It started out with normal logic programs, which are programs that can have negation but not disjunction. Driven by the need of applications, various extensi ...
... Answer Set Programming (ASP) is a new paradigm of constraint-based programming based on logic programming with answer set semantics 17,9,13]. It started out with normal logic programs, which are programs that can have negation but not disjunction. Driven by the need of applications, various extensi ...
Introduction to Discrete Structures Introduction
... than or equal to 100. – The cardinality of the empty set is ||=0 – The sets N, Z, Q, R are all infinite ...
... than or equal to 100. – The cardinality of the empty set is ||=0 – The sets N, Z, Q, R are all infinite ...
Kripke Semantics for Basic Sequent Systems
... rules of LK impose the usual truth-tables in each world, e.g. v(a, ψ ⊃ ϕ) = t iff either v(a, ψ) = f or v(a, ϕ) = t. Example 6. Assume that G contains the two standard rules for intuitionistic implication. Example 4 (3) and the combination of Example 3 (1) and Example 4 (2) together imply that in G- ...
... rules of LK impose the usual truth-tables in each world, e.g. v(a, ψ ⊃ ϕ) = t iff either v(a, ψ) = f or v(a, ϕ) = t. Example 6. Assume that G contains the two standard rules for intuitionistic implication. Example 4 (3) and the combination of Example 3 (1) and Example 4 (2) together imply that in G- ...
Gödel`s correspondence on proof theory and constructive mathematics
... 1950’s, anyone reading Herbrand’s Lemma 3 should have been suspicious. Probably the error escaped public notice for so long simply because Herbrand’s paper itself, important though it was at that time, was badly written and seems not to have been widely studied. Alternative proofs of (versions of) H ...
... 1950’s, anyone reading Herbrand’s Lemma 3 should have been suspicious. Probably the error escaped public notice for so long simply because Herbrand’s paper itself, important though it was at that time, was badly written and seems not to have been widely studied. Alternative proofs of (versions of) H ...
lecture notes in Mathematical Logic
... computer science — and to some hard open problems as well. Logic and computer science Computability theory, also called recursion theory, separated from mathematical logic during the thirties of the last century. In turned out that some parts of logic are of a special nature: they can be entirely ca ...
... computer science — and to some hard open problems as well. Logic and computer science Computability theory, also called recursion theory, separated from mathematical logic during the thirties of the last century. In turned out that some parts of logic are of a special nature: they can be entirely ca ...
Separating classes of groups by first–order sentences
... 2, are first–order by their very definition, most properties cannot even be described by an axiom system (including noneffective ones). Examples of properties of the second kind are: being a torsion group, being finitely generated and being free. Throughout this paper we restrict our attention to co ...
... 2, are first–order by their very definition, most properties cannot even be described by an axiom system (including noneffective ones). Examples of properties of the second kind are: being a torsion group, being finitely generated and being free. Throughout this paper we restrict our attention to co ...
Automata vs. Logics on Data Words
... into equivalent automaton-based specifications, easing, in this way, the various reasoning tasks. Different models of automata which process words over infinite alphabets have been proposed and studied in the literature (see, for instance, the surveys [6, 7]). Pebble automata [8] use special markers ...
... into equivalent automaton-based specifications, easing, in this way, the various reasoning tasks. Different models of automata which process words over infinite alphabets have been proposed and studied in the literature (see, for instance, the surveys [6, 7]). Pebble automata [8] use special markers ...