INTRODUCTION TO LOGIC Natural Deduction
... One way of showing that an argument is valid is to break it down into several steps and to show that one can arrive at the conclusion through some more obvious arguments. It’s not clear one can break down every valid argument into a sequence of steps from a predefined finite set of rules. This is po ...
... One way of showing that an argument is valid is to break it down into several steps and to show that one can arrive at the conclusion through some more obvious arguments. It’s not clear one can break down every valid argument into a sequence of steps from a predefined finite set of rules. This is po ...
Propositional inquisitive logic: a survey
... also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in detail in [7]. In the propositional setting, full translations are possible between the two [25]. In both propositional systems, formulas ...
... also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in detail in [7]. In the propositional setting, full translations are possible between the two [25]. In both propositional systems, formulas ...
Many-Valued Models
... interesting general problem and has received attention from several different areas. In this tutorial we present an elementary but general approach on small finite models, showing their relevance and reviewing some elementary methods and techniques on their uses. There are many significant names in ...
... interesting general problem and has received attention from several different areas. In this tutorial we present an elementary but general approach on small finite models, showing their relevance and reviewing some elementary methods and techniques on their uses. There are many significant names in ...
LOGIC MAY BE SIMPLE Logic, Congruence - Jean
... what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is a strong tendency to consider universal algebra as a general theory of structures. Some people think that algebraic structures are more fundamental than the other ones (see [Papert 1967]) and that they are the proto ...
... what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is a strong tendency to consider universal algebra as a general theory of structures. Some people think that algebraic structures are more fundamental than the other ones (see [Papert 1967]) and that they are the proto ...
sentential logic
... on the reasoning and argument (in the premise-conclusion sense) one finds in personal exchange, advertising, political debate, legal argument, and the social commentary that characterizes newspapers, television, the World Wide Web and other forms of mass media. Formal logic: Formal logic is the stud ...
... on the reasoning and argument (in the premise-conclusion sense) one finds in personal exchange, advertising, political debate, legal argument, and the social commentary that characterizes newspapers, television, the World Wide Web and other forms of mass media. Formal logic: Formal logic is the stud ...
Propositional Logic
... • Express the syllogism as a conditional expression of the form P1 P2 ... Pn C • Create a table with one column for each variable and each subexpression occurring in the formula • Create one row for each possible assignment of T and F to the variables • Fill in the entries for variables with ...
... • Express the syllogism as a conditional expression of the form P1 P2 ... Pn C • Create a table with one column for each variable and each subexpression occurring in the formula • Create one row for each possible assignment of T and F to the variables • Fill in the entries for variables with ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
Normal modal logics (Syntactic characterisations)
... logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntact ...
... logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntact ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... and sentences of the form ‘if A, then B’, usually written with symbols as ‘A B’, or ‘A B’, or ‘A B’. The verbs ‘to imply’, ‘to follow from’, ‘to yield’ and ‘to give’ are all tied to implication (of course, ‘to follow from’ is converse to the others). ‘Entailment’ and ‘to entail’ are used pretty ...
... and sentences of the form ‘if A, then B’, usually written with symbols as ‘A B’, or ‘A B’, or ‘A B’. The verbs ‘to imply’, ‘to follow from’, ‘to yield’ and ‘to give’ are all tied to implication (of course, ‘to follow from’ is converse to the others). ‘Entailment’ and ‘to entail’ are used pretty ...
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 ...
x - Stanford University
... Theorem: If R is transitive, then R-1 is transitive. Proof: Consider any a, b, and c such that aRb and bRc. Since R is transitive, we have aRc. Since aRb and bRc, we have bR-1a and cR-1b. Since we have aRc, we have cR-1a. Thus cR-1b, bR-1a, and cR-1a. ■ This proves ∀a. ∀b. ∀c. (aRb ∧ bRc → cR-1b ∧ b ...
... Theorem: If R is transitive, then R-1 is transitive. Proof: Consider any a, b, and c such that aRb and bRc. Since R is transitive, we have aRc. Since aRb and bRc, we have bR-1a and cR-1b. Since we have aRc, we have cR-1a. Thus cR-1b, bR-1a, and cR-1a. ■ This proves ∀a. ∀b. ∀c. (aRb ∧ bRc → cR-1b ∧ b ...
A brief introduction to Logic and its applications
... Intuitionistic Logic - Stanford Encyclopedia of Philosophy Propositions as Types by Philip Wadler (paper) Propositions as Types by Philip Wadler (video) Introduction to Type Systems by Delphine Demange Why are logical connectives and booleans separate in Coq? ...
... Intuitionistic Logic - Stanford Encyclopedia of Philosophy Propositions as Types by Philip Wadler (paper) Propositions as Types by Philip Wadler (video) Introduction to Type Systems by Delphine Demange Why are logical connectives and booleans separate in Coq? ...
Quantified Equilibrium Logic and the First Order Logic of Here
... slightly different version of QEL where the so-called unique name assumption or UNA is not assumed from the outset but may be added as a special requirement for specific applications. The motivation for relaxing the UNA is to make equilibrium logic more flexible for certain kinds of applications. For i ...
... slightly different version of QEL where the so-called unique name assumption or UNA is not assumed from the outset but may be added as a special requirement for specific applications. The motivation for relaxing the UNA is to make equilibrium logic more flexible for certain kinds of applications. For i ...
Sequentiality by Linear Implication and Universal Quantification
... In this paper we offer a methodology, through a simple and natural case study, which deals with sequentiality in a way which certainly does not have the flavor of continuations. Sequentialization is achieved in linear logic by a controlled form of backchaining, whose non-determinism is eliminated by ...
... In this paper we offer a methodology, through a simple and natural case study, which deals with sequentiality in a way which certainly does not have the flavor of continuations. Sequentialization is achieved in linear logic by a controlled form of backchaining, whose non-determinism is eliminated by ...
Justification logic with approximate conditional probabilities
... 1 whenever the condition has probability 0. Axiom 10 is the formula that states the standard definition of the conditional probability. Finally, the Axioms 11 and 12 (together with Inference Rule 4) give us the relationship between the conditional probability infinitesimally close to the some ration ...
... 1 whenever the condition has probability 0. Axiom 10 is the formula that states the standard definition of the conditional probability. Finally, the Axioms 11 and 12 (together with Inference Rule 4) give us the relationship between the conditional probability infinitesimally close to the some ration ...
Predicate Logic for Software Engineering
... before application of the logical operators to the truthvalues that result. For every value of x other than 0, some component of expression (1) is undefined. With the standard interpretation of logical operators, which are defined only for two-value logics, the value of (1) is not defined except whe ...
... before application of the logical operators to the truthvalues that result. For every value of x other than 0, some component of expression (1) is undefined. With the standard interpretation of logical operators, which are defined only for two-value logics, the value of (1) is not defined except whe ...
Some Principles of Logic
... • If the premises are true then the conclusion is probably but not necessarily true • The conclusion contains information not present, even implicitly, in the premises ...
... • If the premises are true then the conclusion is probably but not necessarily true • The conclusion contains information not present, even implicitly, in the premises ...
Predicate logic
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
Formal logic
... But how and why can we conclude that this last sentence follows from the previous two premises? Or, more generally, how can we determine whether a formula ϕ is a valid consequence of a set of formulas {ϕ1 , . . . , ϕn }? Modern logic offers two possible ways, that used to be fused in the time of syl ...
... But how and why can we conclude that this last sentence follows from the previous two premises? Or, more generally, how can we determine whether a formula ϕ is a valid consequence of a set of formulas {ϕ1 , . . . , ϕn }? Modern logic offers two possible ways, that used to be fused in the time of syl ...
A Proof of Nominalism. An Exercise in Successful
... with structures of particular concrete objects. Now for mathematicians’ deductions of theorems from axioms the interpretation of nonlogical primitives does not matter. In other words it does not matter what these objects are as long as they are particulars forming the right kind of structure. In th ...
... with structures of particular concrete objects. Now for mathematicians’ deductions of theorems from axioms the interpretation of nonlogical primitives does not matter. In other words it does not matter what these objects are as long as they are particulars forming the right kind of structure. In th ...
Lectures on Laws of Supply and Demand, Simple and Compound
... In the case above we will analyze it and show it is always true due to its structure.(You can see this for this simple example just by thinking about it.)In fact it is what is called in logic a tautology. We will let letters A, B or C represent single propositions and we will now investigate the tru ...
... In the case above we will analyze it and show it is always true due to its structure.(You can see this for this simple example just by thinking about it.)In fact it is what is called in logic a tautology. We will let letters A, B or C represent single propositions and we will now investigate the tru ...
Formal Logic, Models, Reality
... this can lead to false conclusions like for instance Bell's inequality. Therefore classical formal logic is not sound when it is applied to a local quantum reality, and classical formal logic cannot be applied directly to a local quantum reality. It can only be applied to set-theoretical semantic mo ...
... this can lead to false conclusions like for instance Bell's inequality. Therefore classical formal logic is not sound when it is applied to a local quantum reality, and classical formal logic cannot be applied directly to a local quantum reality. It can only be applied to set-theoretical semantic mo ...
Journey in being show - horizons
... problems of reason are taken up in The main discussion—Ideas and Journey Objections and counterarguments ...
... problems of reason are taken up in The main discussion—Ideas and Journey Objections and counterarguments ...
GLukG logic and its application for non-monotonic reasoning
... logic satisfying axioms Pos1 and Pos2, and with modus ponens as its unique inference rule, the deduction theorem holds [9]. Multivalued logics An alternative way to define the semantics for a logic is by the use of truth values and interpretations. Multivalued logics generalize the idea of using tru ...
... logic satisfying axioms Pos1 and Pos2, and with modus ponens as its unique inference rule, the deduction theorem holds [9]. Multivalued logics An alternative way to define the semantics for a logic is by the use of truth values and interpretations. Multivalued logics generalize the idea of using tru ...