An Introduction to Prolog Programming
... A Prolog program corresponds to a set of formulas, all of which are assumed to be true. This restricts the range of possible interpretations of the predicate and function symbols appearing in these formulas. The formulas in the translated program may be thought of as the premises in a proof. If Prol ...
... A Prolog program corresponds to a set of formulas, all of which are assumed to be true. This restricts the range of possible interpretations of the predicate and function symbols appearing in these formulas. The formulas in the translated program may be thought of as the premises in a proof. If Prol ...
S. P. Odintsov “REDUCTIO AD ABSURDUM” AND LUKASIEWICZ`S
... to finish an investigation of the class of Lj-extensions with an attempt to overcome it. We try to do it by emerging the class of Lj-extensions in a more general class of paraconsistent logics and pointing out some special property distinguishing extensions of minimal logic in the latter class. We su ...
... to finish an investigation of the class of Lj-extensions with an attempt to overcome it. We try to do it by emerging the class of Lj-extensions in a more general class of paraconsistent logics and pointing out some special property distinguishing extensions of minimal logic in the latter class. We su ...
Consequence Operators for Defeasible - SeDiCI
... than the one used in classical logic. This leads us to consider a specialized consequence operator for Horn-like logics. Formally: De¯nition 3.1 (Consequence Operator Th sld (¡ )). Given an argumentative theory ¡ , we de¯ne Thsld (¡ ) = f[;; fni g]:h j ¡ j»Arg [;; fnig]:hg According to de¯nition 3.1 ...
... than the one used in classical logic. This leads us to consider a specialized consequence operator for Horn-like logics. Formally: De¯nition 3.1 (Consequence Operator Th sld (¡ )). Given an argumentative theory ¡ , we de¯ne Thsld (¡ ) = f[;; fni g]:h j ¡ j»Arg [;; fnig]:hg According to de¯nition 3.1 ...
Kripke completeness revisited
... Goldblatt 2005) where the rôle of the precursors of Kripke semantics is documented in detail. All the anticipations of Kripke’s semantics have been given ample credit, to the extent that very often the neutral terminology of “relational semantics” is preferred. The following quote nicely summarizes ...
... Goldblatt 2005) where the rôle of the precursors of Kripke semantics is documented in detail. All the anticipations of Kripke’s semantics have been given ample credit, to the extent that very often the neutral terminology of “relational semantics” is preferred. The following quote nicely summarizes ...
Propositional logic - Cheriton School of Computer Science
... q , r. (We avoid t, f , T , F for reasons which will become evident.) Compositional sentences will be represented by formulas, which combine atoms with connectives. Formulas are intended to symbolically represent statements in the type of mathematical or logical reasoning we have done in the past. O ...
... q , r. (We avoid t, f , T , F for reasons which will become evident.) Compositional sentences will be represented by formulas, which combine atoms with connectives. Formulas are intended to symbolically represent statements in the type of mathematical or logical reasoning we have done in the past. O ...
An Introduction to Proof Theory - UCSD Mathematics
... is that proofs are social conventions by which mathematicians convince one another of the truth of theorems. That is to say, a proof is expressed in natural language plus possibly symbols and figures, and is sufficient to convince an expert of the correctness of a theorem. Examples of social proofs ...
... is that proofs are social conventions by which mathematicians convince one another of the truth of theorems. That is to say, a proof is expressed in natural language plus possibly symbols and figures, and is sufficient to convince an expert of the correctness of a theorem. Examples of social proofs ...
A Mathematical Introduction to Modal Logic
... Modal logic is a huge research area. Researchers from mathematics, philosophy, computer science, linguistics, political science and economics work on variety of modal logics focusing on numerous different topics with many amazingly different applications. Mathematicians approach it mostly from a mod ...
... Modal logic is a huge research area. Researchers from mathematics, philosophy, computer science, linguistics, political science and economics work on variety of modal logics focusing on numerous different topics with many amazingly different applications. Mathematicians approach it mostly from a mod ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... 1. Γ ⊢LW ∆ iff Π ⊢LW ∆, m m 2. Γ |∼L ∆ iff Π |∼L ∆. 2 This follows from the fact that any such fragment has the classical deduction theorem and an extension of the implication–negation fragment of IPC has the classical deduction theorem iff it is an axiomatic extension (a folklore result; for an exp ...
... 1. Γ ⊢LW ∆ iff Π ⊢LW ∆, m m 2. Γ |∼L ∆ iff Π |∼L ∆. 2 This follows from the fact that any such fragment has the classical deduction theorem and an extension of the implication–negation fragment of IPC has the classical deduction theorem iff it is an axiomatic extension (a folklore result; for an exp ...
Logical Omniscience As Infeasibility - boris
... These postulates, however, have an unrealistic consequence that agents become logically omniscient: not only do the agents know all valid facts, but they must also possess knowledge of all logical consequences of contingent facts they know. This Logical Omniscience Problem was identified in [13, 14, ...
... These postulates, however, have an unrealistic consequence that agents become logically omniscient: not only do the agents know all valid facts, but they must also possess knowledge of all logical consequences of contingent facts they know. This Logical Omniscience Problem was identified in [13, 14, ...
07.1-Reasoning
... language and how they can be used together. • Semantics: Gives meaning to the syntax. Defines how the symbols in the syntax relate to in the real world. ...
... language and how they can be used together. • Semantics: Gives meaning to the syntax. Defines how the symbols in the syntax relate to in the real world. ...
Modal Logic for Artificial Intelligence
... Some rules are very simple: if you can prove ϕ and you can prove ψ, then you can also prove their conjunction ϕ ∧ ψ. Other rules are more complicated. For example, the only way to ‘eliminate’ the disjunction ϕ ∨ ψ is by proving, first that ϕ ∨ ψ, and second, that some conclusion χ can be proven both ...
... Some rules are very simple: if you can prove ϕ and you can prove ψ, then you can also prove their conjunction ϕ ∧ ψ. Other rules are more complicated. For example, the only way to ‘eliminate’ the disjunction ϕ ∨ ψ is by proving, first that ϕ ∨ ψ, and second, that some conclusion χ can be proven both ...
Belief Revision in non
... sense to require that an acceptable belief set be at least consistent, since inconsistency trivialises the notion of consequence in classical logic. However, there is no reason why more specific restrictions should not be imposed on what an acceptable belief set is in classical logic, as it is done ...
... sense to require that an acceptable belief set be at least consistent, since inconsistency trivialises the notion of consequence in classical logic. However, there is no reason why more specific restrictions should not be imposed on what an acceptable belief set is in classical logic, as it is done ...
Introduction to first order logic for knowledge representation
... Is the link that connects the real world with it’s matematical and abstract representation into a mathematical structure. If a certain situation is supposed to be abstractly described by a given structure, then the abstraction connects the elements that participats to the situation, with the compone ...
... Is the link that connects the real world with it’s matematical and abstract representation into a mathematical structure. If a certain situation is supposed to be abstractly described by a given structure, then the abstraction connects the elements that participats to the situation, with the compone ...
A Logical Framework for Default Reasoning
... facts known to be true, and a pool of possible hypotheses, to find an explanation which is a set of instances of possible hypotheses used to predict the expected observations (i.e., together with the facts implies the observations) and is consistent with the facts (i.e., does not predict anything kn ...
... facts known to be true, and a pool of possible hypotheses, to find an explanation which is a set of instances of possible hypotheses used to predict the expected observations (i.e., together with the facts implies the observations) and is consistent with the facts (i.e., does not predict anything kn ...
Structural Multi-type Sequent Calculus for Inquisitive Logic
... of polar questions. For more details on this connection, we refer the reader to [5]. Flat formulas will play an important role in this paper. Below we list some of their properties. Lemma 2.3 (see [3]). For all InqL-formulas φ and ψ, • If ψ is flat, then φ → ψ is flat. In particular, ¬φ is always fl ...
... of polar questions. For more details on this connection, we refer the reader to [5]. Flat formulas will play an important role in this paper. Below we list some of their properties. Lemma 2.3 (see [3]). For all InqL-formulas φ and ψ, • If ψ is flat, then φ → ψ is flat. In particular, ¬φ is always fl ...
Mathematical Induction - Cambridge Computer Lab
... To be valid, this argument cannot go on forever: it requires an ordering; and it must terminate (see lecture 7); this is called a well-founded partial ordering. ...
... To be valid, this argument cannot go on forever: it requires an ordering; and it must terminate (see lecture 7); this is called a well-founded partial ordering. ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... lesson is that there is no deduction without rules of deduction: these rules cannot be entirely replaced by implications (we need at least the rule that enables us to pass from an implication to the corresponding deduction, i.e. modus ponens). The distinction between deduction and implication is not ...
... lesson is that there is no deduction without rules of deduction: these rules cannot be entirely replaced by implications (we need at least the rule that enables us to pass from an implication to the corresponding deduction, i.e. modus ponens). The distinction between deduction and implication is not ...
propositional logic extended with a pedagogically useful relevant
... kinds. This is by no means necessary. One may study ways to remove one of the kinds of paradoxes. Some such ways may have effects on other paradoxes, but not all of them. The logic PCR was devised with the aim of removing only the paradoxes from (iii). In [3], paraconsistency is presented as a means ...
... kinds. This is by no means necessary. One may study ways to remove one of the kinds of paradoxes. Some such ways may have effects on other paradoxes, but not all of them. The logic PCR was devised with the aim of removing only the paradoxes from (iii). In [3], paraconsistency is presented as a means ...
Document
... formula is evaluated to true if and only if the root node of the formula is evaluated to true. In order to determine the value of this node given by an interpretation, one may compute the value of each node in reverse topological order; indeed, the value of the leaves is known – since the leaves are ...
... formula is evaluated to true if and only if the root node of the formula is evaluated to true. In order to determine the value of this node given by an interpretation, one may compute the value of each node in reverse topological order; indeed, the value of the leaves is known – since the leaves are ...
4 - Indiana University–Purdue University Indianapolis
... acknowledgement of experimental intelligence in its most radical implications. At the center of this acknowledgement, we encounter "an experimenter of flesh and blood"— that is, an embodied agent exemplifying experimental intelligence ("What Pragmatism Is" [1905], CP 5.424). This pragmatism is, at o ...
... acknowledgement of experimental intelligence in its most radical implications. At the center of this acknowledgement, we encounter "an experimenter of flesh and blood"— that is, an embodied agent exemplifying experimental intelligence ("What Pragmatism Is" [1905], CP 5.424). This pragmatism is, at o ...
Nonmonotonic Reasoning - Computer Science Department
... Although the logical consequences of formulas in which we believe should also be believed (after all, if we believe that all men are mortal and Socrates is a man, then we have to believe that Socrates is mortal), in commonsense we often employ, in addition to classical logic reasonings, some other m ...
... Although the logical consequences of formulas in which we believe should also be believed (after all, if we believe that all men are mortal and Socrates is a man, then we have to believe that Socrates is mortal), in commonsense we often employ, in addition to classical logic reasonings, some other m ...
Constructing Cut Free Sequent Systems With Context Restrictions
... complexity bounds are therefore increasingly important. This paper explores the method of cut elimination by saturation and extends previous work into two important directions. First, we can now also allow for the propositional base logic to be intuitionistic which allows us to treat a range of logi ...
... complexity bounds are therefore increasingly important. This paper explores the method of cut elimination by saturation and extends previous work into two important directions. First, we can now also allow for the propositional base logic to be intuitionistic which allows us to treat a range of logi ...
Systems of modal logic - Department of Computing
... system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilbert systems: given a set of formulas called axioms and a set of rules of proof, a formula A ...
... system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilbert systems: given a set of formulas called axioms and a set of rules of proof, a formula A ...
One-dimensional Fragment of First-order Logic
... (cf. the formulae PreCons δ and Cons δ in Section 4.1). This way we can encode information concerning accessibility relations by using formulae of MFO. This construction does not work if one tries to maximize both a binary relation R and its complement R at the same time: the problem is that the max ...
... (cf. the formulae PreCons δ and Cons δ in Section 4.1). This way we can encode information concerning accessibility relations by using formulae of MFO. This construction does not work if one tries to maximize both a binary relation R and its complement R at the same time: the problem is that the max ...