M-rank and meager groups
... In this paper we prove that meager types have some of the properties of properly weakly minimal types. This sheds a new light also on the proofs of these properties in the weakly minimal case. Suppose p is a meager type. Since p is non-trivial, we get a clp -triangle. Given a clp -triangle {a0 , a1 ...
... In this paper we prove that meager types have some of the properties of properly weakly minimal types. This sheds a new light also on the proofs of these properties in the weakly minimal case. Suppose p is a meager type. Since p is non-trivial, we get a clp -triangle. Given a clp -triangle {a0 , a1 ...
Conditional XPath
... formula. More precisely, each node wff is equivalent to an F Otree formula in one free variable, and each path wff to an F Otree formula in two free variables. But not only there is a bound on the number of free variables in the corresponding first order formula, we can also bound the total number o ...
... formula. More precisely, each node wff is equivalent to an F Otree formula in one free variable, and each path wff to an F Otree formula in two free variables. But not only there is a bound on the number of free variables in the corresponding first order formula, we can also bound the total number o ...
A Logical Framework for Default Reasoning
... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...
... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...
Intuitionistic and Modal Logic
... • Theorem For finite Γ, Γ ` IPC ϕ iff ϕ is valid in all finite Kripke models of Γ for IPC. • Proof. The proof can be done by filtration. We will not do that here. Or by reducing the whole discussion to the set of subformulas of Γ ∪ {ϕ} (a so-called adequate set, both in the definition of the (reduce ...
... • Theorem For finite Γ, Γ ` IPC ϕ iff ϕ is valid in all finite Kripke models of Γ for IPC. • Proof. The proof can be done by filtration. We will not do that here. Or by reducing the whole discussion to the set of subformulas of Γ ∪ {ϕ} (a so-called adequate set, both in the definition of the (reduce ...
Cardinal Invariants of Analytic P-Ideals
... to understand the structure of the ideal itself. Significant progress in understanding the way in which the structure of an ideal affects the structure of its quotient has been done by I. Farah [Fa1, Fa2, Fa3, Fa4, Fa5]. Typically (but not always) the quotients P(ω)/I, where I is an analytic P-ideal ...
... to understand the structure of the ideal itself. Significant progress in understanding the way in which the structure of an ideal affects the structure of its quotient has been done by I. Farah [Fa1, Fa2, Fa3, Fa4, Fa5]. Typically (but not always) the quotients P(ω)/I, where I is an analytic P-ideal ...
The Journal of Functional and Logic Programming The MIT Press
... Thus, although in one way or another all CLP systems use more than one constraint domain, they do not freely allow mixed terms or constraints, that is, constraint expressions containing nonvariable symbols from different signatures. Notable exceptions are uninterpreted function symbols, which can ge ...
... Thus, although in one way or another all CLP systems use more than one constraint domain, they do not freely allow mixed terms or constraints, that is, constraint expressions containing nonvariable symbols from different signatures. Notable exceptions are uninterpreted function symbols, which can ge ...
A causal approach to nonmonotonic reasoning
... lated causal approaches to representing actions and change have been suggested in [23,36, 38], to mention only a few. From the point of view of the present study, the causal reasoning constitutes an important conceptual shift in the general framework of explanatory nonmonotonic reasoning, since it i ...
... lated causal approaches to representing actions and change have been suggested in [23,36, 38], to mention only a few. From the point of view of the present study, the causal reasoning constitutes an important conceptual shift in the general framework of explanatory nonmonotonic reasoning, since it i ...
A Pebble Weighted Automata and Weighted Logics
... automata and word transducers appear as instances of that framework, which found its way into numerous application areas such as natural language processing and speech recognition or digital image compression (see [Droste et al. 2009, Part IV]). A logical characterization of weighted automata, howev ...
... automata and word transducers appear as instances of that framework, which found its way into numerous application areas such as natural language processing and speech recognition or digital image compression (see [Droste et al. 2009, Part IV]). A logical characterization of weighted automata, howev ...
Incompleteness
... arity associated with it, with is a positive integer. The exact meaning of the arity is made clear below, but it is intending to denote the arity of a relation or function to which the symbol R or f corresponds. Example 1. The language of set theory consists of a single binary relation symbol P. The ...
... arity associated with it, with is a positive integer. The exact meaning of the arity is made clear below, but it is intending to denote the arity of a relation or function to which the symbol R or f corresponds. Example 1. The language of set theory consists of a single binary relation symbol P. The ...
Theories and uses of context in knowledge representation and
... “Whenever we write an axiom, a critic can say that the axiom is true only in a certain context. With a little ingenuity the critic can usually devise a more general context in which the precise form of the axiom doesn’t hold. Looking at human reasoning as reflected in language emphasizes this point. ...
... “Whenever we write an axiom, a critic can say that the axiom is true only in a certain context. With a little ingenuity the critic can usually devise a more general context in which the precise form of the axiom doesn’t hold. Looking at human reasoning as reflected in language emphasizes this point. ...
A KE Tableau for a Logic of Formal Inconsistency - IME-USP
... We now prove a Hintikka’s Lemma for mCi downward saturated sets: Lemma 1. (Hintikka’s Lemma) Every mCi downward saturated set is satisfiable. Proof. For any downward saturated set DS, we can easily construct an mCi valuation v such that for every signed formula SX in the set, v(SX) = 1. How can we g ...
... We now prove a Hintikka’s Lemma for mCi downward saturated sets: Lemma 1. (Hintikka’s Lemma) Every mCi downward saturated set is satisfiable. Proof. For any downward saturated set DS, we can easily construct an mCi valuation v such that for every signed formula SX in the set, v(SX) = 1. How can we g ...
A Qualitative Theory of Dynamic Interactive Belief Revision
... The simplest and most natural way to define a connected pre-order on a Cartesian product from connected pre-orders on each of the components is to use either the lexicographic or the anti-lexicographic order. Our choice is the second, which we regard as the natural generalization of the AGM theory, ...
... The simplest and most natural way to define a connected pre-order on a Cartesian product from connected pre-orders on each of the components is to use either the lexicographic or the anti-lexicographic order. Our choice is the second, which we regard as the natural generalization of the AGM theory, ...
The Pure Calculus of Entailment Author(s): Alan Ross Anderson and
... logicians somewhat as follows: "The two-valued propositional calculus sanctions as valid many of the obvious and satisfactory inferences which we recognize intuitively as valid, such as (A--.B-TIC)-GAR-B-*.A-C,2 and A--B-.B--C-.A-C; it consequently suggests itself as a candidate for a formal analysi ...
... logicians somewhat as follows: "The two-valued propositional calculus sanctions as valid many of the obvious and satisfactory inferences which we recognize intuitively as valid, such as (A--.B-TIC)-GAR-B-*.A-C,2 and A--B-.B--C-.A-C; it consequently suggests itself as a candidate for a formal analysi ...
Syntax and Semantics of Dependent Types
... We will henceforth freely suppress type annotations if this increases readability. For instance, we may write x: :M or even x:M instead of x: :M . We sometimes omit a prevailing context ? and thus write ` J instead of ? ` J . We write ` J if we want to emphasise that a judgement holds in th ...
... We will henceforth freely suppress type annotations if this increases readability. For instance, we may write x: :M or even x:M instead of x: :M . We sometimes omit a prevailing context ? and thus write ` J instead of ? ` J . We write ` J if we want to emphasise that a judgement holds in th ...
pTopic8
... its operators, that satisfy its axioms. The set NAT = {0,1,2, ...} is a model of N. The term algebra of a theory consists of the language (i.e. the set of strings of symbols) generated by considering the theory’s signature as a grammar. The term algebra of N is the set {‘zero’, ‘succ zero’, ‘succ su ...
... its operators, that satisfy its axioms. The set NAT = {0,1,2, ...} is a model of N. The term algebra of a theory consists of the language (i.e. the set of strings of symbols) generated by considering the theory’s signature as a grammar. The term algebra of N is the set {‘zero’, ‘succ zero’, ‘succ su ...
The Herbrand Manifesto
... What makes it all work is that the language of Relational Logic has a clearly defined semantics, which gives meaning to logical connectives and quantifiers. This allows us to know that we are using those connectives and quantifiers correctly; and it allows to be sure that, in our reasoning, we are d ...
... What makes it all work is that the language of Relational Logic has a clearly defined semantics, which gives meaning to logical connectives and quantifiers. This allows us to know that we are using those connectives and quantifiers correctly; and it allows to be sure that, in our reasoning, we are d ...
A pragmatic dialogic interpretation of bi
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
ICS 353: Design and Analysis of Algorithms
... only if they have the same truth value no matter which predicates are substituted into these statements and which domain of discourse is used for the variables in these propositional functions. ...
... only if they have the same truth value no matter which predicates are substituted into these statements and which domain of discourse is used for the variables in these propositional functions. ...
Dedukti
... the realm of formal proofs is today a tower of Babel, just like the realm of theories was, before the design of predicate logic. The reason why these formalisms have not been defined as theories in predicate logic is that predicate logic, as a logical framework, has several limitations, that make it ...
... the realm of formal proofs is today a tower of Babel, just like the realm of theories was, before the design of predicate logic. The reason why these formalisms have not been defined as theories in predicate logic is that predicate logic, as a logical framework, has several limitations, that make it ...
Propositional Logic
... proofs or refutations. This use of a logical language is called proof theory. In this case, a set of facts called axioms and a set of deduction rules (inference rules) are given, and the object is to determine which facts follow from the axioms and the rules of inference. When using logic as a proof ...
... proofs or refutations. This use of a logical language is called proof theory. In this case, a set of facts called axioms and a set of deduction rules (inference rules) are given, and the object is to determine which facts follow from the axioms and the rules of inference. When using logic as a proof ...
Constraint propagation
... all variables that occur in them. B1,…,Bn are called body-atoms of the Horn clause; A is the head of the Horn clause. n may be 0: in this case we say that the Horn clause is a fact. ...
... all variables that occur in them. B1,…,Bn are called body-atoms of the Horn clause; A is the head of the Horn clause. n may be 0: in this case we say that the Horn clause is a fact. ...
A survey on Interactive Theorem Proving
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
First-Order Theorem Proving and VAMPIRE
... The rest of this paper is organised as follows. Sections 2-5 describe the underlining principles of first-order theorem proving and address various issues that are only implemented in VAMPIRE. Sections 6-11 present new and unconventional applications of first-order theorem proving implemented in VAM ...
... The rest of this paper is organised as follows. Sections 2-5 describe the underlining principles of first-order theorem proving and address various issues that are only implemented in VAMPIRE. Sections 6-11 present new and unconventional applications of first-order theorem proving implemented in VAM ...
thèse - IRIT
... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...
... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...
On modal logics of group belief
... The aim of this work is to advance the state of the art on artificial institutions and normative MASs by proposing a logical model in which the existence and the dynamics of an institution (norms, rules, institutional facts, etc) are determined by the individual and collective attitudes of the agent ...
... The aim of this work is to advance the state of the art on artificial institutions and normative MASs by proposing a logical model in which the existence and the dynamics of an institution (norms, rules, institutional facts, etc) are determined by the individual and collective attitudes of the agent ...