Expressiveness of Logic Programs under the General Stable Model
... set solvers. For example, in the propositional case, there have been a number of works that implemented answer set solving by reducing the existence of answer sets to the satisfiability of classical propositional logic, see, e.g., [Lin and Zhao 2004; Lierler and Maratea 2004]. In this work, we are i ...
... set solvers. For example, in the propositional case, there have been a number of works that implemented answer set solving by reducing the existence of answer sets to the satisfiability of classical propositional logic, see, e.g., [Lin and Zhao 2004; Lierler and Maratea 2004]. In this work, we are i ...
Dependence Logic
... We can replace “all M” by “some M with more than one element in the universe” in the above corollary. Note that in particular we do not have for all X 6= ∅: M |=X ¬ =(x0, x1) ⇐⇒ M 6|=X =(x0, x1). Example 10 Every team X, the domain of which contains xi and xj is of type xi = xj ∨ ¬xi = xj , as we ca ...
... We can replace “all M” by “some M with more than one element in the universe” in the above corollary. Note that in particular we do not have for all X 6= ∅: M |=X ¬ =(x0, x1) ⇐⇒ M 6|=X =(x0, x1). Example 10 Every team X, the domain of which contains xi and xj is of type xi = xj ∨ ¬xi = xj , as we ca ...
Strong Normalisation for a Gentzen-like Cut
... As can be seen, these cut-reductions are restricted so that they are applicable only if the immediate subterms of the cuts freshly introduce the names and conames corresponding to the cut-formulae. Without this restriction bound names or bound co-names might become free during cut-elimination, as de ...
... As can be seen, these cut-reductions are restricted so that they are applicable only if the immediate subterms of the cuts freshly introduce the names and conames corresponding to the cut-formulae. Without this restriction bound names or bound co-names might become free during cut-elimination, as de ...
The Computer Modelling of Mathematical Reasoning Alan Bundy
... theorem proving’ techniques could be readily brought into a Resolution framework, and how this helped us to relate the various techniques – creating coherence from confusion. In order to achieve this goal I have taken strong historical liberties in my descriptions of the work of Boyer and Moore, Gel ...
... theorem proving’ techniques could be readily brought into a Resolution framework, and how this helped us to relate the various techniques – creating coherence from confusion. In order to achieve this goal I have taken strong historical liberties in my descriptions of the work of Boyer and Moore, Gel ...
MATH20302 Propositional Logic
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
Termination of Higher-order Rewrite Systems
... Implementing abstract data types; Automated theorem proving, especially for equational logic; Proving completeness of axiomatizations for algebras; Proving consistency of proof calculi for logics. These tasks can be divided into practical and theoretical applications. In theoretical applicat ...
... Implementing abstract data types; Automated theorem proving, especially for equational logic; Proving completeness of axiomatizations for algebras; Proving consistency of proof calculi for logics. These tasks can be divided into practical and theoretical applications. In theoretical applicat ...
Goal-directed Proof Theory
... deduction in few categories. Most of the ideas and methods for non-classical deduction have been derived from their classical counterpart. We have analytic methods such as tableaux, systems based on Gentzen's calculi, methods which extend and reformulate classical resolution, translation based metho ...
... deduction in few categories. Most of the ideas and methods for non-classical deduction have been derived from their classical counterpart. We have analytic methods such as tableaux, systems based on Gentzen's calculi, methods which extend and reformulate classical resolution, translation based metho ...
Soundness and Completeness for Sentence Logic Trees
... a rule produces shorter sentences. At the end we have at least one branch on which all the sentences are true in I. But this branch must be open. Since all the sentences along the branch are true in I, no sentence and its negation can both appear on the branch! In sum, if the original sentences are ...
... a rule produces shorter sentences. At the end we have at least one branch on which all the sentences are true in I. But this branch must be open. Since all the sentences along the branch are true in I, no sentence and its negation can both appear on the branch! In sum, if the original sentences are ...
Sets, Logic, Computation
... shorthand symbols for these, and think through the general properties of sets, relations, and functions in order to do that. If you are not used to thinking mathematically and to formulating mathematical proofs, then think of the first part on set theory as a training ground: all the basic definitio ...
... shorthand symbols for these, and think through the general properties of sets, relations, and functions in order to do that. If you are not used to thinking mathematically and to formulating mathematical proofs, then think of the first part on set theory as a training ground: all the basic definitio ...
A causal approach to nonmonotonic reasoning
... that covers significant parts of general nonmonotonic reasoning. In this respect, it forms a viable non-epistemic alternative to default and modal nonmonotonic logics. The logical foundations of the suggested formalism will be built in the framework of an inference system for causal rules, called pr ...
... that covers significant parts of general nonmonotonic reasoning. In this respect, it forms a viable non-epistemic alternative to default and modal nonmonotonic logics. The logical foundations of the suggested formalism will be built in the framework of an inference system for causal rules, called pr ...
Tableau-based decision procedure for the full
... branching-time logic considered in [7] and this paper, was presented. In our view (to be explained further), however, [11] should be seen as a contribution to the complexity-theoretic analysis of the temporal-epistemic logics rather than to the development of efficient decision procedures for them. ...
... branching-time logic considered in [7] and this paper, was presented. In our view (to be explained further), however, [11] should be seen as a contribution to the complexity-theoretic analysis of the temporal-epistemic logics rather than to the development of efficient decision procedures for them. ...
On modal logics of group belief
... Some conceptual clarifications of the concept of acceptance qua member of an institution are needed because of the crucial role it plays in explaining the maintenance of social institutions. Several authors have emphasized the difference between acceptance and belief as particular kinds of individua ...
... Some conceptual clarifications of the concept of acceptance qua member of an institution are needed because of the crucial role it plays in explaining the maintenance of social institutions. Several authors have emphasized the difference between acceptance and belief as particular kinds of individua ...
One-dimensional Fragment of First-order Logic
... 2 Antti Kuusisto acknowledges that this work was carried out during a tenure of the ERCIM “Alain Bensoussan” Fellowship Programme, and that the research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement number 2460 ...
... 2 Antti Kuusisto acknowledges that this work was carried out during a tenure of the ERCIM “Alain Bensoussan” Fellowship Programme, and that the research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement number 2460 ...
Sets, Logic, Computation
... shorthand symbols for these, and think through the general properties of sets, relations, and functions in order to do that. If you are not used to thinking mathematically and to formulating mathematical proofs, then think of the first part on set theory as a training ground: all the basic definitio ...
... shorthand symbols for these, and think through the general properties of sets, relations, and functions in order to do that. If you are not used to thinking mathematically and to formulating mathematical proofs, then think of the first part on set theory as a training ground: all the basic definitio ...
Teach Yourself Logic 2017: A Study Guide
... L3. If you have taken an elementary logic course based on a substantial text like the ones mentioned in just a moment, then you should be well prepared. Here then, for those that need them, are two initial suggestions of formal logic books that start from scratch and go far enough to provide a good ...
... L3. If you have taken an elementary logic course based on a substantial text like the ones mentioned in just a moment, then you should be well prepared. Here then, for those that need them, are two initial suggestions of formal logic books that start from scratch and go far enough to provide a good ...
