1 Introduction to Categories and Categorical Logic
... For computer scientists: category theory gives a precise handle on important notions such as compositionality, abstraction, representationindependence, genericity and more. Otherwise put, it provides the fundamental mathematical structures underpinning many key programming concepts. For logicians: c ...
... For computer scientists: category theory gives a precise handle on important notions such as compositionality, abstraction, representationindependence, genericity and more. Otherwise put, it provides the fundamental mathematical structures underpinning many key programming concepts. For logicians: c ...
Algebraic foundations for the semantic treatment of inquisitive content
... alternative semantics makes suitable predictions about the semantic behavior of the corresponding connectives and quantifiers in a variety of typologically unrelated natural languages. However, even though we have thus obtained a much more accurate characterization of the meaning of the relevant con ...
... alternative semantics makes suitable predictions about the semantic behavior of the corresponding connectives and quantifiers in a variety of typologically unrelated natural languages. However, even though we have thus obtained a much more accurate characterization of the meaning of the relevant con ...
The Computer Modelling of Mathematical Reasoning Alan Bundy
... • Part III consists of five rational reconstructions of theorem proving techniques or programs. Each was selected because it contributes an important partial solution to the problem of guiding the search for a proof. This part is the heart of the book. • Part IV is a two chapter discussion of aspect ...
... • Part III consists of five rational reconstructions of theorem proving techniques or programs. Each was selected because it contributes an important partial solution to the problem of guiding the search for a proof. This part is the heart of the book. • Part IV is a two chapter discussion of aspect ...
Syllogistic Analysis and Cunning of Reason in
... for instance tried to construct the whole mathematics by three mother structures, all three structures are defined by syllogisms. Some researchers in philosophy of mathematics use a special syllogism called complementarity in searching for mathematical knowledge. According to Otte, mathematical prac ...
... for instance tried to construct the whole mathematics by three mother structures, all three structures are defined by syllogisms. Some researchers in philosophy of mathematics use a special syllogism called complementarity in searching for mathematical knowledge. According to Otte, mathematical prac ...
Consequence relations and admissible rules
... for a sentence A to logically follow from a set of sentences Γ. He arrived at the definition that this is so if and only if every model of the sentences in Γ is a model of A. This led to the introduction and study of consequence relations, which are relations between sets of expressions and expressi ...
... for a sentence A to logically follow from a set of sentences Γ. He arrived at the definition that this is so if and only if every model of the sentences in Γ is a model of A. This led to the introduction and study of consequence relations, which are relations between sets of expressions and expressi ...
Reasoning about Complex Actions with Incomplete Knowledge: A
... We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing actions as well as complex actions definitions. Our starting point is the modal logic programming language for reasoning about actions presented in [6]. Such la ...
... We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing actions as well as complex actions definitions. Our starting point is the modal logic programming language for reasoning about actions presented in [6]. Such la ...
A Yabloesque paradox in epistemic game theory
... liar paradoxes, there has been suggested a variety of non-classical models which satisfy the BK paradox (Başkent 2015). The BK paradox is formalized using a bimodal language and relational models. We briefly review the logical framework on which we shall build our new paradox. The model M = (U a , ...
... liar paradoxes, there has been suggested a variety of non-classical models which satisfy the BK paradox (Başkent 2015). The BK paradox is formalized using a bimodal language and relational models. We briefly review the logical framework on which we shall build our new paradox. The model M = (U a , ...
Constraint Logic Programming with Hereditary Harrop Formula
... different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et al., 1996). Their implementation relies on the combination of SLD resolution w ...
... different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et al., 1996). Their implementation relies on the combination of SLD resolution w ...
Yablo`s paradox
... in Yablo’s paradox. I shall also show that Yablo’s paradox has exactly the same structure as all the familiar paradoxes of set theory and semantics. To put the discussion into context, think, first, of the standard Liar paradox, ‘This sentence is not true’. Writing T as the truth predicate, then the ...
... in Yablo’s paradox. I shall also show that Yablo’s paradox has exactly the same structure as all the familiar paradoxes of set theory and semantics. To put the discussion into context, think, first, of the standard Liar paradox, ‘This sentence is not true’. Writing T as the truth predicate, then the ...
On the futility of criticizing the neoclassical maximization hypothesis
... Tautologies are statements which are true by virtue of their logical form alone – that is, one cannot even conceive of how they could ever be false. For example, the statement ‘I am here or I am not here’ is true regardless of the meaning of the non-logical words ‘I’ or ‘here’. There is no conceivab ...
... Tautologies are statements which are true by virtue of their logical form alone – that is, one cannot even conceive of how they could ever be false. For example, the statement ‘I am here or I am not here’ is true regardless of the meaning of the non-logical words ‘I’ or ‘here’. There is no conceivab ...
Constraint propagation
... Select some Bi atom from the body of Goal Select some clause Bi C1 C2 … Cm from T Replace Bi in the body of Goal by C1 C2 … Cm Until Goal = false or no more Selections possible ...
... Select some Bi atom from the body of Goal Select some clause Bi C1 C2 … Cm from T Replace Bi in the body of Goal by C1 C2 … Cm Until Goal = false or no more Selections possible ...
Set theory and logic
... In Chapter 8 several axiomatic theories which fall within the realm of modern algebra are introduced. The primary purpose is to enable us to give self-contained characterizations in turn of the system of integers, of rational numbers, and, finally, of real numbers. This is clone in the last three se ...
... In Chapter 8 several axiomatic theories which fall within the realm of modern algebra are introduced. The primary purpose is to enable us to give self-contained characterizations in turn of the system of integers, of rational numbers, and, finally, of real numbers. This is clone in the last three se ...
Lecture Notes on Sequent Calculus
... We have already mentioned that antecedents in sequent proofs are persistent: once an assumption is made, it is henceforth usable above the inference that introduces it. Sequent proofs also obey the important subformula property: if we examine the complete or partial proof above a sequent, we observe ...
... We have already mentioned that antecedents in sequent proofs are persistent: once an assumption is made, it is henceforth usable above the inference that introduces it. Sequent proofs also obey the important subformula property: if we examine the complete or partial proof above a sequent, we observe ...
Logical Theories and Compatible Operations
... second-order theory). The second approach is also useful for classes of nite structures as not every such class has a decidable theory. In order to process structures by algorithmic means, a nite encoding of the structure is required. Such encodings are trivial when structures are nite (though on ...
... second-order theory). The second approach is also useful for classes of nite structures as not every such class has a decidable theory. In order to process structures by algorithmic means, a nite encoding of the structure is required. Such encodings are trivial when structures are nite (though on ...
Discrete Mathematics: Chapter 2, Predicate Logic
... Sentential Logic: Complete But Deficient We noted at the outset that our Natural Deduction System of Sentential Logic is both sound and complete (see Section 1.5). It is sound because if a sentence can be proved from a set of premises, then it is a logical consequence of those premises: If P − Q, th ...
... Sentential Logic: Complete But Deficient We noted at the outset that our Natural Deduction System of Sentential Logic is both sound and complete (see Section 1.5). It is sound because if a sentence can be proved from a set of premises, then it is a logical consequence of those premises: If P − Q, th ...