Conjunctive normal form - Computer Science and Engineering
... boolean formula expressed in Conjunctive Normal Form, such that the formula is true. The k-SAT problem is the problem of finding a satisfying assignment to a boolean formula expressed in CNF in which each disjunction contains at most k variables. 3-SAT is NP-complete (like any other k-SAT problem wi ...
... boolean formula expressed in Conjunctive Normal Form, such that the formula is true. The k-SAT problem is the problem of finding a satisfying assignment to a boolean formula expressed in CNF in which each disjunction contains at most k variables. 3-SAT is NP-complete (like any other k-SAT problem wi ...
A Logical Expression of Reasoning
... This issue plays a central role in our approach. It is important to characterize defective theories through the detection of cycles: rules relevant to the derivation of each other exception or to their own exception. A cyclic theory may have more than one or even none extension (in some fortuitous c ...
... This issue plays a central role in our approach. It is important to characterize defective theories through the detection of cycles: rules relevant to the derivation of each other exception or to their own exception. A cyclic theory may have more than one or even none extension (in some fortuitous c ...
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 ...
full text (.pdf)
... included, among many others, extensions to modal logics (Kurz 2001; Schröder 2005, 2008; Schröder and Pattinson 2007) and structural operational semantics (Klin 2007; Turi and Plotkin 1997). However, most attention has been devoted to bisimulation proofs of equality between coinductively defined ob ...
... included, among many others, extensions to modal logics (Kurz 2001; Schröder 2005, 2008; Schröder and Pattinson 2007) and structural operational semantics (Klin 2007; Turi and Plotkin 1997). However, most attention has been devoted to bisimulation proofs of equality between coinductively defined ob ...
Nonmonotonic Reasoning - Computer Science Department
... reasoning is true in all intended interpretations (or models) in which the premises are true. A ”completeness and correctness theorem” for a system says that the ”safe” rules of deduction in the textbooks generate exactly all those conclusions from premises which are true in every interpretation in ...
... reasoning is true in all intended interpretations (or models) in which the premises are true. A ”completeness and correctness theorem” for a system says that the ”safe” rules of deduction in the textbooks generate exactly all those conclusions from premises which are true in every interpretation in ...
07.1-Reasoning
... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...
... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...
Handling Exceptions in nonmonotonic reasoning
... Our proceeding to determine the theorems of a defeasible axiomatic basis is, then, to impose some conditions upon candidates to be considered an expansion. The theory associated with an expansion is what we call an admissible set of theorems of a defeasible axiomatic basis, this is our equivalent no ...
... Our proceeding to determine the theorems of a defeasible axiomatic basis is, then, to impose some conditions upon candidates to be considered an expansion. The theory associated with an expansion is what we call an admissible set of theorems of a defeasible axiomatic basis, this is our equivalent no ...
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 ...
Slides for Rosen, 5th edition
... A proposition (p, q, r, …) is simply a statement (i.e., a declarative sentence) with a definite meaning, having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). (However, you might not know the actual truth value, and it might be situation-dependent.) ...
... A proposition (p, q, r, …) is simply a statement (i.e., a declarative sentence) with a definite meaning, having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). (However, you might not know the actual truth value, and it might be situation-dependent.) ...
Justification logic with approximate conditional probabilities
... {ϕ → CP≤r+ n1 (α, β) | n ≥ 1−r , n ∈ N} infer ϕ → CP≈r (α, β). 5. From P≤0 α infer ¬α, for α ∈ FmlJ . Axiom 3, putting > instead of β, says that the probability of each formula being satisfied in some set of worlds is at least 0, and we can easily infer (using ¬α instead of α) that the upper bound i ...
... {ϕ → CP≤r+ n1 (α, β) | n ≥ 1−r , n ∈ N} infer ϕ → CP≈r (α, β). 5. From P≤0 α infer ¬α, for α ∈ FmlJ . Axiom 3, putting > instead of β, says that the probability of each formula being satisfied in some set of worlds is at least 0, and we can easily infer (using ¬α instead of α) that the upper bound i ...
Logic and Sets
... which is just a long-winded way of saying that there are only finitely many Mersenne primes. The point to be made from the above discussion is that the abstract logical form of a mathematical statement or argument is independent of its particular content. The rules of logic provide a means for analy ...
... which is just a long-winded way of saying that there are only finitely many Mersenne primes. The point to be made from the above discussion is that the abstract logical form of a mathematical statement or argument is independent of its particular content. The rules of logic provide a means for analy ...
Proof Theory for Propositional Logic
... majority of sentences you hear and speak have never been spoken before and will never be spoken before, how do you understand what they mean? Some philosophers, like Donald Davidson,2 pose this issue in terms of human finitude. For any natural language there is no upper bound on the length of senten ...
... majority of sentences you hear and speak have never been spoken before and will never be spoken before, how do you understand what they mean? Some philosophers, like Donald Davidson,2 pose this issue in terms of human finitude. For any natural language there is no upper bound on the length of senten ...
The Logic of Compound Statements
... A proposition p is necessary for q if q cannot be true without it: ~p → ~q (equivalent to q → p is a tautology). Example: It is necessary for a student to have a 3.0 GPA in the ...
... A proposition p is necessary for q if q cannot be true without it: ~p → ~q (equivalent to q → p is a tautology). Example: It is necessary for a student to have a 3.0 GPA in the ...
The logic and mathematics of occasion sentences
... of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantic ...
... of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantic ...
Proof theory of witnessed G¨odel logic: a
... logic?. Our answer is: a relaxed notion of the subformula property and the extraction of minimal information from proofs of simple existential statements, i.e., a weak form of Herbrand theorem. We call ∃-analytic any calculus satisfying these properties. The calculi for Gödel logic in [2, 21, 22] a ...
... logic?. Our answer is: a relaxed notion of the subformula property and the extraction of minimal information from proofs of simple existential statements, i.e., a weak form of Herbrand theorem. We call ∃-analytic any calculus satisfying these properties. The calculi for Gödel logic in [2, 21, 22] a ...
Discrete Mathematics - Lecture 4: Propositional Logic and Predicate
... Every statement is either TRUE or FALSE There are logical connectives ∨, ∧, ¬, =⇒ and ⇐⇒ . Two logical statements can be equivalent if the two statements answer exactly in the same way on every input. To check whether two logical statements are equivalent one can do one of the following: Checking th ...
... Every statement is either TRUE or FALSE There are logical connectives ∨, ∧, ¬, =⇒ and ⇐⇒ . Two logical statements can be equivalent if the two statements answer exactly in the same way on every input. To check whether two logical statements are equivalent one can do one of the following: Checking th ...
INTRODUCTORY LOGIC – Glossary of key terms
... Formal logic that deals with reasoning from examples or experience to probable conclusions. Inductive conclusions are either strong or weak. Informal fallacy Lesson 33, page 257 A popular but invalid (or unhelpful) form of argument. Informal logic Introduction, page 5 Logic that deals with operation ...
... Formal logic that deals with reasoning from examples or experience to probable conclusions. Inductive conclusions are either strong or weak. Informal fallacy Lesson 33, page 257 A popular but invalid (or unhelpful) form of argument. Informal logic Introduction, page 5 Logic that deals with operation ...
Chapter 6: The Deductive Characterization of Logic
... Note carefully that we allow zero-place rules. A well-known example in elementary logic is the reflexivity rule for identity (given “nothing”, one is entitled to write down ‘τ = τ’ for any singular term). The existence of zero-place rules is critical if we are to have a non-trivial notion of proof, ...
... Note carefully that we allow zero-place rules. A well-known example in elementary logic is the reflexivity rule for identity (given “nothing”, one is entitled to write down ‘τ = τ’ for any singular term). The existence of zero-place rules is critical if we are to have a non-trivial notion of proof, ...
Rich Chapter 5 Predicate Logic - Computer Science
... So we appear to be forced to move to first-order predicate logic (or just predicate logic, since we do not discuss higher order theories in this chapter) as a way of representing knowledge because it permits representations of things that cannot reasonably be represented in prepositional logic. In ...
... So we appear to be forced to move to first-order predicate logic (or just predicate logic, since we do not discuss higher order theories in this chapter) as a way of representing knowledge because it permits representations of things that cannot reasonably be represented in prepositional logic. In ...
Counterfactuals
... ordering for two spheres of a given world is always well-defined. Lewis’ conditions are, quite obviously, non-trivial, and he defends each in turn: (C) The constraint C asserts that the base world is more similar to itself than it is to any other world; while Lewis does consider a case where another ...
... ordering for two spheres of a given world is always well-defined. Lewis’ conditions are, quite obviously, non-trivial, and he defends each in turn: (C) The constraint C asserts that the base world is more similar to itself than it is to any other world; while Lewis does consider a case where another ...
Geometry Fall Final Exam -
... The point of concurrency of the perpendicular bisectors of the sides of a triangle which locates the center of a circle that circumscribes the triangle is called the ____. ...
... The point of concurrency of the perpendicular bisectors of the sides of a triangle which locates the center of a circle that circumscribes the triangle is called the ____. ...
what are we to accept, and what are we to reject
... From Paradox [3]. This is a wonderful book: it’s clear and precise, interesting and engaging, and deep and important all at once. Truth and the paradoxes comprise a very difficult field in which to work. Nonetheless, the work in that field is deep and important. Field advances the state of the art o ...
... From Paradox [3]. This is a wonderful book: it’s clear and precise, interesting and engaging, and deep and important all at once. Truth and the paradoxes comprise a very difficult field in which to work. Nonetheless, the work in that field is deep and important. Field advances the state of the art o ...
A proposition is any declarative sentence (including mathematical
... When we say “P implies Q” or even “If P then Q,” we normally mean that the statement P, if true, somehow causes or forces the statement Q to be true. In mathematics, most conditionals convey this kind of causality, but it is not a requirement. In logic (and therefore in mathematics), the truth or fa ...
... When we say “P implies Q” or even “If P then Q,” we normally mean that the statement P, if true, somehow causes or forces the statement Q to be true. In mathematics, most conditionals convey this kind of causality, but it is not a requirement. In logic (and therefore in mathematics), the truth or fa ...