Combining Paraconsistent Logic with Argumentation
... Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to those of Caminada and Amgoud [3], to characterise cases under which the trivialisation problem is avoided (called the postulates of non-interference and crashresistance). The problem can then be reformula ...
... Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to those of Caminada and Amgoud [3], to characterise cases under which the trivialisation problem is avoided (called the postulates of non-interference and crashresistance). The problem can then be reformula ...
Classical Propositional Logic
... Completeness A Henkin-style Completeness Proof for Natural Deduction ...
... Completeness A Henkin-style Completeness Proof for Natural Deduction ...
Relevant and Substructural Logics
... and with hypotheses from among the set X. A proof from hypotheses is simply a list of formulas, each of which is either an hypothesis, an axiom, or one which follows from earlier formulas in the list by means of a rule. In Orlov’s system, the only rule is modus ponens. We will see later that this is ...
... and with hypotheses from among the set X. A proof from hypotheses is simply a list of formulas, each of which is either an hypothesis, an axiom, or one which follows from earlier formulas in the list by means of a rule. In Orlov’s system, the only rule is modus ponens. We will see later that this is ...
Argumentations and logic
... can think that we have deduced a conclusion thought to be false from a hypothesis augmented by premises thought to be true and then discover that the hypothesis itself played no role in the reasoning. This means that we have arrived at an argumentation that seems to deduce a conclusion thought to be ...
... can think that we have deduced a conclusion thought to be false from a hypothesis augmented by premises thought to be true and then discover that the hypothesis itself played no role in the reasoning. This means that we have arrived at an argumentation that seems to deduce a conclusion thought to be ...
Reading 2 - UConn Logic Group
... connection of his realizability with BHK interpretation. It is also worth mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). The Curry-Howard isomorphism transliterates natural derivations in Int to ...
... connection of his realizability with BHK interpretation. It is also worth mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). The Curry-Howard isomorphism transliterates natural derivations in Int to ...
Decision procedures in Algebra and Logic
... Algebraic structure positive definite. See Birkhoff and MacLane (1979: 369). • Graded vector space: a vector space such that the members of M have a direct sum decomposition. See graded algebra below. Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field in ...
... Algebraic structure positive definite. See Birkhoff and MacLane (1979: 369). • Graded vector space: a vector space such that the members of M have a direct sum decomposition. See graded algebra below. Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field in ...
In order to define the notion of proof rigorously, we would have to
... In order to define the notion of proof rigorously, we would have to define a formal language in which to express statements very precisely and we would have to set up a proof system in terms of axioms and proof rules (also called inference rules). We will not go into this; this would take too much t ...
... In order to define the notion of proof rigorously, we would have to define a formal language in which to express statements very precisely and we would have to set up a proof system in terms of axioms and proof rules (also called inference rules). We will not go into this; this would take too much t ...
Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012
... many readers, particularly those not already well-versed in the subject, will find that work an uncompromising and difficult one. By far the best introduction so far to the subject is Michael Dunn’s survey article, ‘Relevant Logic and Entailment’.3 The present book does not attempt to compete with D ...
... many readers, particularly those not already well-versed in the subject, will find that work an uncompromising and difficult one. By far the best introduction so far to the subject is Michael Dunn’s survey article, ‘Relevant Logic and Entailment’.3 The present book does not attempt to compete with D ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... von Wright’s original work in preference logic, in order to motivate some of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of po ...
... von Wright’s original work in preference logic, in order to motivate some of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of po ...
A Logical Expression of Reasoning
... intended to be able) to carry truth on all the way from premises, once it is there, to conclusion. Being truthfulness such a precious good, a reasoning that does not assure its integrity has not deserved respect and serious concern from the tradition. That is why for so long, at least until Hume [12 ...
... intended to be able) to carry truth on all the way from premises, once it is there, to conclusion. Being truthfulness such a precious good, a reasoning that does not assure its integrity has not deserved respect and serious concern from the tradition. That is why for so long, at least until Hume [12 ...
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 ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... remove the proposition “a” from the KB. Another choice would be to remove the proposition “a→b” from the KB. Alternatively, one could ignore the revision and keep the KB as is. Finally, several other options can be imagined, such as replacing a proposition of the KB with another, or dropping both pr ...
... remove the proposition “a” from the KB. Another choice would be to remove the proposition “a→b” from the KB. Alternatively, one could ignore the revision and keep the KB as is. Finally, several other options can be imagined, such as replacing a proposition of the KB with another, or dropping both pr ...
Non-Classical Logic
... For example, in your first course on propositional or sentential logic, you learned that the language consisted of propositional parameters or variables, p0 , p1 , etc., symbols such as “∨”, “¬”, and that they be combined to form complex formulæ such as “¬(p1 ∨ ¬ p0 )”. This was syntax. You also lea ...
... For example, in your first course on propositional or sentential logic, you learned that the language consisted of propositional parameters or variables, p0 , p1 , etc., symbols such as “∨”, “¬”, and that they be combined to form complex formulæ such as “¬(p1 ∨ ¬ p0 )”. This was syntax. You also lea ...
Modal Languages and Bounded Fragments of Predicate Logic
... expressive modal formalisms (Venema 1991, De Rijke 1993). Of course, one can also study the effects of special frame restrictions – but we must leave this issue for further investigation, except for some passing remarks. What precisely are fragments of classical first-order logic showing “modal” beh ...
... expressive modal formalisms (Venema 1991, De Rijke 1993). Of course, one can also study the effects of special frame restrictions – but we must leave this issue for further investigation, except for some passing remarks. What precisely are fragments of classical first-order logic showing “modal” beh ...
MODAL LANGUAGES AND BOUNDED FRAGMENTS OF
... Here, of course, the key observation lies in the zigzag clauses. If some world u in M+ is modally equivalent with v in N+ , and Rus holds, then the following set of formulas is finitely satisfiable in N+ , v : {Rvx} plus the full modal theory of s in M+ . But then, by ω-saturation, some world t must ...
... Here, of course, the key observation lies in the zigzag clauses. If some world u in M+ is modally equivalent with v in N+ , and Rus holds, then the following set of formulas is finitely satisfiable in N+ , v : {Rvx} plus the full modal theory of s in M+ . But then, by ω-saturation, some world t must ...
Modal Consequence Relations
... of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation between sets of formulae and a single formula. A consequence relation ` specifies which arguments are valid; the argument ...
... of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation between sets of formulae and a single formula. A consequence relation ` specifies which arguments are valid; the argument ...
Fichte`s Legacy in Logic
... follows I focus my attention on two logicians in particular: Moritz Wm. Drobisch and Franz Brentano -- a heroic logical normal and a logical subversive. Moritz Drobisch (1802-1896) was, in effect, Fichte’s logical grandson, by way of Johann Friedrich Herbart (1776-1841) -- the founder and namesake o ...
... follows I focus my attention on two logicians in particular: Moritz Wm. Drobisch and Franz Brentano -- a heroic logical normal and a logical subversive. Moritz Drobisch (1802-1896) was, in effect, Fichte’s logical grandson, by way of Johann Friedrich Herbart (1776-1841) -- the founder and namesake o ...
The substitutional theory of logical consequence
... For formalized languages the substitutional account of logical validity has largely been superseded by the proof-theoretic and the model-theoretic approaches. According to the proof-theoretic or inferentialist conception, roughly, an argument is valid if and only if the conclusion can be derived fro ...
... For formalized languages the substitutional account of logical validity has largely been superseded by the proof-theoretic and the model-theoretic approaches. According to the proof-theoretic or inferentialist conception, roughly, an argument is valid if and only if the conclusion can be derived fro ...
Intuitionistic and Modal Logic
... that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more than logic, since mathematics can be reduced to it, a view supported by Russell (not a Platonist) at th ...
... that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more than logic, since mathematics can be reduced to it, a view supported by Russell (not a Platonist) at th ...
Many-Valued Logic
... It is normal in the sense that it agrees with two-valued logic on the values assigned all combinations of 1s and 0s, and it is uniform in the sense that it maintains that, in defining the connectives, if a compound has the same value whether a component is true or false, it also has that value if th ...
... It is normal in the sense that it agrees with two-valued logic on the values assigned all combinations of 1s and 0s, and it is uniform in the sense that it maintains that, in defining the connectives, if a compound has the same value whether a component is true or false, it also has that value if th ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
LINEAR LOGIC AS A FRAMEWORK FOR SPECIFYING SEQUENT
... In this paper, we make use of linear logic as a meta-logic and find that we can specify a variety of proof systems for object-level systems. By making use of classical linear logic, we are able to capture not only natural deduction proof systems but also many sequent calculus proof systems. We will ...
... In this paper, we make use of linear logic as a meta-logic and find that we can specify a variety of proof systems for object-level systems. By making use of classical linear logic, we are able to capture not only natural deduction proof systems but also many sequent calculus proof systems. We will ...
Higher Order Logic - Theory and Logic Group
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
Higher Order Logic - Indiana University
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... (1946a, 1946b, 1947) and Rudolf Carnap (1946, 1947) who were the first to formulate axiomatic systems that combined quantification theory with (S5- and S4-type) modal logic. The attempts to interpret quantified modal logic by means of formal semantic methods also began with Carnap (1946, 1947), wher ...
... (1946a, 1946b, 1947) and Rudolf Carnap (1946, 1947) who were the first to formulate axiomatic systems that combined quantification theory with (S5- and S4-type) modal logic. The attempts to interpret quantified modal logic by means of formal semantic methods also began with Carnap (1946, 1947), wher ...
Willard Van Orman Quine
Willard Van Orman Quine (/kwaɪn/; June 25, 1908 – December 25, 2000) (known to intimates as ""Van"") was an American philosopher and logician in the analytic tradition, recognized as ""one of the most influential philosophers of the twentieth century."" From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. A recent poll conducted among analytic philosophers named Quine as the fifth most important philosopher of the past two centuries. He won the first Schock Prize in Logic and Philosophy in 1993 for ""his systematical and penetrating discussions of how learning of language and communication are based on socially available evidence and of the consequences of this for theories on knowledge and linguistic meaning."" In 1996 he was awarded the Kyoto Prize in Arts and Philosophy for his ""outstanding contributions to the progress of philosophy in the 20th century by proposing numerous theories based on keen insights in logic, epistemology, philosophy of science and philosophy of language.""Quine falls squarely into the analytic philosophy tradition while also being the main proponent of the view that philosophy is not conceptual analysis but the abstract branch of the empirical sciences. His major writings include ""Two Dogmas of Empiricism"" (1951), which attacked the distinction between analytic and synthetic propositions and advocated a form of semantic holism, and Word and Object (1960), which further developed these positions and introduced Quine's famous indeterminacy of translation thesis, advocating a behaviorist theory of meaning. He also developed an influential naturalized epistemology that tried to provide ""an improved scientific explanation of how we have developed elaborate scientific theories on the basis of meager sensory input."" He is also important in philosophy of science for his ""systematic attempt to understand science from within the resources of science itself"" and for his conception of philosophy as continuous with science. This led to his famous quip that ""philosophy of science is philosophy enough."" In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the ""Quine–Putnam indispensability thesis,"" an argument for the reality of mathematical entities.