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 ...
George VOUTSADAKIS CATEGORICAL ABSTRACT ALGEBRAIC
... Around the end of the nineteenth and the beginning of the last century, several authors considered the process of coordinatization of various axiomatically defined abstract geometries. Among them were the affine plane geometry, affine plane geometry with the Desargues and Pappus properties, projecti ...
... Around the end of the nineteenth and the beginning of the last century, several authors considered the process of coordinatization of various axiomatically defined abstract geometries. Among them were the affine plane geometry, affine plane geometry with the Desargues and Pappus properties, projecti ...
Effectively Polynomial Simulations
... rise to interesting new questions, eg. does Resolution effectively-p simulate Extended Frege, answering which seems to require strengthening and extending known proof techniques and developing new connections between computational complexity and proof complexity. ...
... rise to interesting new questions, eg. does Resolution effectively-p simulate Extended Frege, answering which seems to require strengthening and extending known proof techniques and developing new connections between computational complexity and proof complexity. ...
a semantic perspective - Institute for Logic, Language and
... as a tool for talking about structures or models. But what kind of structures can modal logic talk about? There is no single answer. For example, modal logic can be given an algebraic semantics, and under this interpretation modal logic is a tool for talking about what are known as boolean algebras ...
... as a tool for talking about structures or models. But what kind of structures can modal logic talk about? There is no single answer. For example, modal logic can be given an algebraic semantics, and under this interpretation modal logic is a tool for talking about what are known as boolean algebras ...
The Project Gutenberg EBook of The Algebra of Logic, by Louis
... of Aristotle, given new life and power by being dressed up in the wonderful almost magicalarmour and accoutrements of Algebra. In less than seventy years, logic, to use an expression of De Morgan's, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians wo ...
... of Aristotle, given new life and power by being dressed up in the wonderful almost magicalarmour and accoutrements of Algebra. In less than seventy years, logic, to use an expression of De Morgan's, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians wo ...
Discrete Mathematics
... In each case, the missing connectives can be defined in terms of the connectives that are present. For example, I left out exclusive or, P ⊕ Q, but P ⊕ Q = (P ∧ ¬ Q) ∨ ¬ P ∧ Q ...
... In each case, the missing connectives can be defined in terms of the connectives that are present. For example, I left out exclusive or, P ⊕ Q, but P ⊕ Q = (P ∧ ¬ Q) ∨ ¬ P ∧ Q ...
A Pebble Weighted Automata and Weighted Logics
... et al. 2001] consider counting and aggregate quantifiers for first-order logic to talk about two-sorted structures. Roughly speaking, they allow us to specify how often a Boolean formula shall be satisfied, or to sum up over all elements satisfying a property. However, a sentence still defines a lan ...
... et al. 2001] consider counting and aggregate quantifiers for first-order logic to talk about two-sorted structures. Roughly speaking, they allow us to specify how often a Boolean formula shall be satisfied, or to sum up over all elements satisfying a property. However, a sentence still defines a lan ...
Canonicity and representable relation algebras
... After 1997, Venema conjectured ‘no’, because of: Fact 4 (Venema, 1997) RRA has no Sahlqvist axiomatisation. Sahlqvist equations are defined syntactically. They are paradigm examples of canonical axioms. E,g., all positive equations are Sahlqvist. Venema knew Sahlqvist equations are preserved under ( ...
... After 1997, Venema conjectured ‘no’, because of: Fact 4 (Venema, 1997) RRA has no Sahlqvist axiomatisation. Sahlqvist equations are defined syntactically. They are paradigm examples of canonical axioms. E,g., all positive equations are Sahlqvist. Venema knew Sahlqvist equations are preserved under ( ...
Propositional Logic
... § Propositional Logic (Boolean logic) § First-Order Logic (aka first-order predicate calculus) § Non-Monotonic Logic § Markov Logic A logic includes: § syntax: what is a correctly-formed sentence? § semantics: what is the meaning of a sentence? § Inference procedure (reasoning, entailment): w ...
... § Propositional Logic (Boolean logic) § First-Order Logic (aka first-order predicate calculus) § Non-Monotonic Logic § Markov Logic A logic includes: § syntax: what is a correctly-formed sentence? § semantics: what is the meaning of a sentence? § Inference procedure (reasoning, entailment): w ...
19_pl
... If a problem domain can be represented formally, then a decision maker can use logical reasoning to make rational decisions Many types of logic Propositional Logic (Boolean logic) First-Order Logic (aka first-order predicate calculus) Non-Monotonic Logic Markov Logic A logic includes: synt ...
... If a problem domain can be represented formally, then a decision maker can use logical reasoning to make rational decisions Many types of logic Propositional Logic (Boolean logic) First-Order Logic (aka first-order predicate calculus) Non-Monotonic Logic Markov Logic A logic includes: synt ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
Measure Quantifier in Monadic Second Order Logic
... Monadic Second Order logic (MSO) is the extension of first order logic with quantification over subsets of the domain. For example, when interpreted over the relational structure (ω, <) of natural numbers with the standard order, the formula ∃A.∀n.∃m.(n < m ∧ m ∈ A) expresses the existence of set A ...
... Monadic Second Order logic (MSO) is the extension of first order logic with quantification over subsets of the domain. For example, when interpreted over the relational structure (ω, <) of natural numbers with the standard order, the formula ∃A.∀n.∃m.(n < m ∧ m ∈ A) expresses the existence of set A ...
Combinaison des logiques temporelle et déontique pour la
... In order to formally specify a security policy, it is natural to reason about time on the one hand, and obligations, permissions, and prohibitions on the other hand. Indeed, we have to express for instance the permission to access a resource for a certain period, the obligation to release a resource ...
... In order to formally specify a security policy, it is natural to reason about time on the one hand, and obligations, permissions, and prohibitions on the other hand. Indeed, we have to express for instance the permission to access a resource for a certain period, the obligation to release a resource ...
the fundamentals of abstract mathematics
... “hypotheses”). In this chapter, we will introduce three basic ingredients of Logic: assertions, deductions, and validity. 1A. Assertions, deductions, and validity Here is one possible deduction: Hypotheses: (1) It is raining heavily. (2) If you do not take an umbrella, you will get soaked. Conclusio ...
... “hypotheses”). In this chapter, we will introduce three basic ingredients of Logic: assertions, deductions, and validity. 1A. Assertions, deductions, and validity Here is one possible deduction: Hypotheses: (1) It is raining heavily. (2) If you do not take an umbrella, you will get soaked. Conclusio ...
REVERSE MATHEMATICS, WELL-QUASI
... and algebraic geometry but with the connections between Noetherian spaces and the theory of well-quasi-orders. Goubault-Larrecq in [GL07], motivated by possible applications to verification problems as explained in [GL10], provided several results demonstrating that Noetherian spaces can be thought ...
... and algebraic geometry but with the connections between Noetherian spaces and the theory of well-quasi-orders. Goubault-Larrecq in [GL07], motivated by possible applications to verification problems as explained in [GL10], provided several results demonstrating that Noetherian spaces can be thought ...
Proof Pearl: Defining Functions over Finite Sets
... (useful for defining minimum). Both require distinct fold functionals and their own theory. In the development of these theories we demonstrate locales, a lesserknown Isabelle feature. As we go along, we compare our approach with the one in HOL4 [7] and PVS [13], both of which provide their own libra ...
... (useful for defining minimum). Both require distinct fold functionals and their own theory. In the development of these theories we demonstrate locales, a lesserknown Isabelle feature. As we go along, we compare our approach with the one in HOL4 [7] and PVS [13], both of which provide their own libra ...